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Н Новости

Intro RL

Для меня разобраться в базовых концепциях Reinforcement Learning оказалось не так просто, особенно сложными оказались функции Беллмана. Эта статья — моя попытка систематизировать материал и объяснить себе (и, возможно, другим), что, откуда и почему берется. Будет здорово, если она поможет кому-то разложить все по полочкам.

¯\_(ツ)_/¯

Полезные ссылки:
Practical RL (ШАД) (самые полезные материалы были тут)
Лекция №15 "Обучение с подкреплением"
Тренировки. Лекция 3: Введение в обучение с подкреплением
Тренировки. Лекция 4: Q-learning, Deep Q-learning
Тренировки. Лекция 5: Современные методы обучения с подкреплением. Advantage actor critic, RLHF
11.1. Обучение с подкреплением

Мой тг канал: Not Magic Neural Networks

Содержание

1. Intro
2. Определения
3. Cross-Entropy Method, CEM
4. Markov decision process, MDP
5. Награда (reward) и коэффициент дисконтирования

6. Оценочные функции
6.1. Backup Tree & динамическое программирование
6.2. State-value function и Policy Evaluation
6.3. Policy Improvement и action-value function
6.4. Уравнения оптимальности Беллмана

7. Generalized Policy iteration

1. Intro

Дрессировка щенка

На гифке щенок учится через игру: он пробует разные действия, наблюдает за реакцией человека и запоминает, что именно приносит ему вкусняшку. Когда за правильное поведение он получает награду, у него формируется связь между действием и результатом — «сделал правильно → получил вкусняшку». Так шаг за шагом песик осваивает новые команды, учится понимать, чего от него ждут, и радостно повторяет то, что приносит успех.

Такое обучение называется Reinforcement Learning (RL) — обучение методом проб и ошибок. Термин reinforcement ("подкрепление") заимствован из поведенческой психологии и терапии и означает последствия (награду или наказание), которые увеличивают или уменьшают вероятность повторения определённого поведения.

Главное отличие RL от обучения с учителем (supervised learning) состоит в том, что этот подход не требует заранее размеченных данных и не опирается на дифференцируемую функцию потерь.

Опишем более формально рассуждения выше:
Пусть у нас есть агент, который взаимодействует с окружающей средой. В каждый момент времени агент наблюдает состояние среды и, опираясь на эти наблюдения, совершает действие. В результате действия состояние среды изменяется.
Процедуру выбора действия будем называть стратегией (или политикой).
За каждое свое действие агент получает награду (или штраф).
Цель агента – изменить свою политику так, чтобы получить максимальную награду. Процесс взаимодействия агента и среды задается динамикой среды, а серия взаимодействий агента со средой от начального до терминального состояния называется эпизодом.

В примере выше, агентом является сам щенок. Он наблюдает за окружающей средой — своим дрессировщиком — и, следуя своей политике, выбирает, какие действия совершить. Если песик всё сделал правильно, его хвалят и угощают вкусняшкой — это и есть награда. Если же действие оказалось неправильным, награды нет, и песику приходится изменить свою политику, пробуя другие действия. Со временем он учится выбирать такую последовательность действий, которая приносит как можно больше вкусняшек — то есть максимизирует свою суммарную награду.

2. Определения:

Reinforcement Learning — обучение методом проб и ошибок.
Agent (агент) — интеллектуальная система (программа, робот, алгоритм), которая принимает решения и совершает действия в некоторой среде с целью достижения определённых целей.
Environment (среда) — всё, с чем взаимодействует агент: внешний мир, в котором происходят события и изменения в ответ на действия агента.
Observation (наблюдение) — информация, которую агент получает от среды в каждый момент времени .
$a = \pi (s)$ : active (действие агента) — конкретное решение или команда, которую агент выбирает и выполняет в среде с целью повлиять на неё.
: stage (состояние) – описание текущей ситуации, в которой находится агент.
$\pi (a|s)$ : policy (политика или стратегия поведения агента) — вероятностное распределение действий при условии состояния .
$R_{s,s'}^{a}$ : Reward (награда) — цели и желания, закодированные в скалярном сигнале. Награда может быть положительной, отрицательной (штрафом) или нейтральной. Она зависит от текущего состояния среды , выбранного агентом действия и следующего состояния среды .
$G = \sum R_i$ : return или cumulative reward – просуммированый по времени reward.
$G \rightarrow \max_{\pi}$ : цель агента — максимизировать return с помощью оптимальной политики.
Траектория — цепочка генерируемых в ходе взаимодействия случайных величин

3. Cross-Entropy Method, CEM

Кросс-энтропийный метод (Cross-Entropy Method, CEM) — это простой алгоритм, который используется для поиска оптимальной политики путем итеративного улучшения выборки решений.

Для простоты будем считать, что количество состояний и действий нашей задачи – конечно. Тогда политику $\pi$ можно задать с помощью матрицы у которой по строкам — состояния, а по столбцам — действия.

Алгоритм:

Инициализируем политику $\pi$ (случайным или равновероятным образом).
$\pi = \begin{array}{c|cccc} & a_1 & a_2 & \dots & a_n \\ \hline s_1 & P(a_1|s_1) & P(a_2|s_1) & \dots & P(a_n|s_1) \\ s_2 & P(a_1|s_2) & P(a_2|s_2) & \dots & P(a_n|s_2) \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ s_m & P(a_1|s_m) & P(a_2|s_m) & \dots & P(a_n|s_m) \end{array} = A_{s,a}$
Семплируем сессий с данной политикой.
Выбираем сессий с наибольшей наградой (элиту).
$\text{Elite} = [(s_0, a_0), (s_1, a_1), \ldots, (s_M, a_M)]$
Обновляем политику в соответствии с элитой (повышаем вероятность "правильных" действий, согласно элитным):
$\pi_{\text{new}}(a \mid s) = \frac{ \sum\limits_{s_t, a_t \in \text{Elite}} [s_t = s][a_t = a] }{ \sum\limits_{s_t, a_t \in \text{Elite}} [s_t = s] } = \frac{\text{Сколько раз совершали действие a в состоянии s}}{\text{Сколько раз были в состоянии s}}$
Возвращаемся к шагу 2.

Step-by-step view (Practical_RL)

Approximate cross-entropy method

Можно рассмотреть выбор действия при условии состояния (политику) как задачу классификации: $\pi(a|s) = f_{\theta}(a,s)$ , где $f_{\theta}$ может быть случайным лесом, логрегрессей или нейронной сетью.

Аналогично, семплируем сессий и выбираем из них элитных.

Максимизируем правдоподобие элитных сессий:

$\pi(a|s)_{\text{new}} = argmax_{\pi} \sum_{s,a \in \text{elite}} \log \pi(a_i|s_i)$

Отсюда название "метод кросс-энтропии": максимизация правдопобия = минимазация кросс-энтропии.

Из плюсов, кросс-энтропийный метод легко реализовывать и он дает хорошие результаты, устойчив относительно сходимости в локальный оптимум. Однако, этот метод рассматривает среду как «чёрный ящик» – то есть он ничего не знает о том что внутри среды происходит.

Ноутбук потыкать (вторая домашка с тренировок).

Попробуем улучшить его, учитывая внутреннюю структуру среды. Эта структура описывается Марковским свойством.

4. Markov decision process, MDP

Чаще всего, после совершения действия агентом, состояние среды будет меняться. Например, при игре в шахматы агент должен учитывать то, что после его хода и хода оппонента позиция на доске изменится.

Нам нужно определить некий процесс, в котором агент последовательно переходит из состояния в состояние в зависимости от своих действий, и в некоторых состояниях получая награды.

Марковский процесс (цепь) — это кортеж (S,P) , где — множество состояний, — матрица переходов (transition matrix), состоящая из вероятностей оказаться в состоянии , при условии, что среда находилась в состоянии .

$P_{ss'} = P(S_{t+1} = s' \mid S_{t} = s)$

Марковское свойство — это условная независимость от истории, кроме как от текущего состояния и текущего действия, для награды и следующего состояния.

Среда является Марковской, когда награда и следующее состояние зависят только от текущего состояния среды .

Марковский процессом принятия решений (MDP) – это кортеж $(\mathbb S,\mathbb A,\mathbb R,\mathbb P,\gamma)$ , где $\mathbb S$ — множество состояний, $\mathbb A$ — множество действий, $\mathbb P_{ss'}^{a}$ — матрица переходов, $\mathbb R_{ss'}^{a}$ — функция награды, $\gamma$ — коэффициент дисконтирования.

$MDP = (\mathbb S,\mathbb A,\mathbb R,\mathbb P,\gamma)$

5. Награда (reward) и коэффициент дисконтирования

Суммарная награда (cumulative reward) — это сумма всех наград на всех шагах агента:

$G_t = \sum_t^T R_i$

где R_i — мгновенная награда (immediate reward),— конец эпизода.

Цель агента — максимизировать кумулятивную награду. То есть, это наше оптимизируемое значение.

Легко заметить, что цели агента и наши собственные цели могут сильно различаться. Более того, правильно задать функцию награды так, чтобы она действительно отражала наши намерения, на практике оказывается совсем непросто.

Например, если агент получает награду за экономию топлива, то он перестаёт двигаться вообще, ведь так он минимизирует расход и получает максимум награды. Если агент получает награду за быстрое прибытие в пункт назначения, то он начинает превышать скорость и нарушать правила, что опасно. Если агент получает награду на каждом шаге за приближение к цели, то его оптимальной политикой будет блуждание по кругу, собирая бесконечную сумму наград, вместо того чтобы прийти к цели и закончить эпизод.

Для того чтобы избежать ситуацию, когда агент накапливает бесконечную сумму наград, используется коэффициент дисконтирования $\gamma$ , который показывает, насколько ценными являются будущие награды на текущий момент:

$G_t = \sum R_t + \gamma (R_{t-1} + \gamma R_{t-2} + \ldots) = R_t + \gamma G_{t-1}$

При $\gamma \rightarrow 0$ смотрим на меньшее количество шагов назад, при $\gamma = 0$ получим "жадный алгоритм".
При $\gamma \rightarrow 1$ смотрим на большее количество шагов, при $\gamma=1$ смотрим на всю историю.
При $\gamma = 0.99$ видим около 100 шагов назад, при $\gamma = 0.95$ около 20 шагов, при $\gamma = 0.9$ около 10 шагов.

Важно понимать, что выбор $\gamma$ не гиперпараметр алгоритма, а часть задачи. Оптимальное поведение агента для разных $\gamma$ может отличаться.

Таким образом, новая цель агента — максимизировать суммарную дисконтированную награду.

Однако, дисконтированная награда лишь отчасти убирает проблему зацикливания, но не решает ее полностью.

Ещё один пример: если агент, играющий в шахматы, получает награду за каждую съеденную фигуру, то оптимальной политикой для него станет стратегия, при которой он старается захватить как можно больше фигур. Однако такая политика не гарантирует победу — агент может съедать много фигур, но в итоге проигрывать партию.

С одной стороны, функция награды должна максимально соответствовать целям, которые мы хотим, чтобы агент достигал. Кажется логичным награждать только за конечный успех — например, за победу. Но в таком случае возникает проблема разреженной награды (sparse rewards): агент получает обратную связь лишь в конце эпизода и не может понять, какие конкретно действия привели к успеху.

Чтобы облегчить обучение, применяют приём под названием reward shaping — формирование награды. Идея заключается в том, чтобы добавить вспомогательную функцию-подсказку , которая помогает агенту двигаться в нужном направлении. Обычно F(s,a,s′ ) получается как разность потенциалов, где – текущее состояние, – действие, – будущее состояние.

$F(s,a,s') = \gamma \Phi(s') - \Phi(s)$

— оригинальная награда
— shaping-функция (дополнительная награда), которая зависит от состояний и/или действий.
$\Phi(s)$ — potential function, «потенциал» состояния, который показывает, насколько хорошо находиться в этом состоянии.

Таким образом, если агент движется в направлении «лучших» состояний, он получает дополнительную награду. Если идет «назад», получает штраф.

6. Оценочные функции

6.1. Backup Tree & динамическое программирование

Давайте построим дерево следующей структуры:
— на светлой вершине лежит текущее состояние
— на темных вершинах лежат действия
— после действия, на ребре лежит награда
— оказываемся в новом состоянии (на светлой вершине)
Оптимальной политикой будет путь, содержащий максимальную сумму наград от корня до листа.

Такая задача решается с помощью динамического программирования: идем от листьев к корню дерева и тащим за собой максимальную сумму наград. Но для того чтобы протащить значение будущей награды вверх по дереву, нужно ввести два понятия: функция полезности состояния и функция полезности состояния действия (state-value и action-value functions).

Backup Tree

Функции ценности — это функции состояний (или пар состояний-действий), которые оценивают, насколько хорошо агенту находиться в данном состоянии (или насколько хорошо выполнять данное действие в данном состоянии).

6.2. State-value function

Пусть мы хотим понять, насколько хорошее наше текущее состояние .
Цель агента – максимизировать суммарную дисконтированную награду. Тогда пусть "хорошестю текущего состояния " будет ожидаемая суммарная дисконтированная награда, если мы будем следовать нашей политике $\pi$ .
При этом, путь от текущего состояния до терминального содержит очень много случайностей: начальное состояние, действие из нашей политики, следующее состояние, следующая награда... Эту "хорошесть" называют state-value function.

State-value function $v_{\pi}$ — это математическое ожидание суммарной дисконтированной награды , которую агент получит, находясь в состоянии и следуя политике $\pi$ .

Для фиксированной политики $\pi$ мы можем посчитать суммарную дисконтированную награду честно взяв мат. ожидание:

$v_\pi(s) \triangleq \mathbb{E}_\pi \big[ G_t \mid S_t = s \big] =$

$= \mathbb{E}\pi \left[ R_t + \gamma G_{t+1} \mid S_t = s \right] =$

$= \sum_a \pi(a \mid s) \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma \mathbb{E}\pi \big[ G_{t+1} \mid S_{t+1} = s' \big] \Big] =$

– текущее состояние, – следующее состояние.
Стохастичность политики $\pi(a|s)$ в том что агент может выбирать разные действия с ненулевыми вероятностями.
Стохастичность окружения в том что следующее состояние и награда могут быть случайными.
$\gamma \mathbb{E}\pi \big[ G_{t+1} \mid S_{t+1} = s' \big] \Big]$ — дисконтированное мат. ожидание от будущей награды, параметризованное только будущим действием , которое можно свернуть в $v_\pi(s')$ .

$= \sum_a \pi(a \mid s) \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

$[1] \quad \quad v_\pi(s) = \sum_a \pi(a \mid s) \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

Или так:

$[1] \quad \quad v_{\pi}(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a) + \gamma v^{\pi}(s') \right]$

Обнаружив рекуррентное соотношение, мы поняли как пересчитать $v_\pi(s)$ имея $v_\pi(s')$ .

v(s) (функция качества состояния) — средняя награда, которую получит агент, начиная играть с состояния при следовании политики $\pi$ (оценка, насколько хорошо находиться в состоянии ).

Посчитаем v-функцию для текущего состояния s

Пусть мы имеем следующее дерево и находимся в состоянии (в корне).

Bellman equation on a backup tree

Наша политика $\pi$ говорит, что из текущего состояния выберем действие a_0 с вероятностью 0.7 , а действие a_1 c вероятностью 0.3 .
Совершив действие a_0 награда будет , совершив действие a_1 , награда будет .
Действие a_0 приведет нас в терминальное состояние с вероятностью . Действие a_1 приведет нас в состояние s_0 с вероятностью 0.1 , а в s_1 с вероятностью 0.9 .
Значение функций-состояния $v_{\pi}$ в состояниях s_0 и s_1 нам уже известны.
Давайте посчитаем функцию-состояния $v_{\pi}$ для нашего текущего состояния без учета дисконтирования (для корня дерева).

Просто считаем математическое ожидание:

$V(s) = \color{red}{0.3} \left[ \color{blue}{0.1} (\color{yellow}{1} + \color{green}{10}) + \color{blue}{0.9} (\color{yellow}{1} + \color{green}{-10}) \right] + \color{red}{0.7} \left[ \color{blue}{1.0} (\color{yellow}{0} + \color{green}{0}) \right] = 2.76$

Если мы посчитаем -функцию для каждого состояния , то сможем понять как нам надо поменять нашу политику $\pi$ , чтобы она стала оптимальной: нам просто надо идти туда, где награда больше.

Как же можно посчитать -функцию? Рассмотрим два способа: матричный и метод простой итерации.

Policy Evaluation: matrix way (первый способ)

Посмотрим еще раз на уравнение [1] : $v_{\pi}(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a) + \gamma v_{\pi}(s') \right]$

Разделим его на две части: $v_{\pi}(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a)\right] + \mathbb{E}_{a} \mathbb{E}_{s'} \gamma \left[v_{\pi}(s') \right]$

Проиндексировав все состояния, посмотрим на -функцию как на вектор: каждому состоянию будет соответствовать свое значение v(s) .

Математическое ожидание награды по действиям и по следующему состоянию обозначим матрицей $B = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a)\right]$ – вектор средних наград.

Вторую часть запишем в следующем виде: $\gamma P v = \gamma \mathbb{E}_{a} \mathbb{E}_{s'} \left[v_{\pi}(s') \right]$ , где $P_{s \times s}$ – матрица содержащая вероятности перехода из одного состояния в другое, то есть $P_{ij} = p(s_j | s_i)$ – вероятность попасть в состояние s_j при условии s_i с учетом текущей политики $\pi$ .

Тогда уравнение [1] можно записать $v_{\pi} = B + \gamma P v_{\pi}$ .
Значения для, $\gamma$ и нам известны. Решим матричное уравнение относительно $v_{\pi}$ :

$(I - \gamma P) v_{\pi} = B$

$v_{\pi} = B(I - \gamma P)^{-1}$

Данное уравнение всегда разрешимо (это гарантирует $0 < \gamma \leq 1$ ), но вычисление обратной матрицы может быть дорого и неустойчиво.

Policy Evaluation: fixed-point iteration (второй способ)

Можно решить уравнение [1] методом простой итерации (fixed-point iteration).

Метод заключается в том что мы будем обновлять оценку v(s) до тех пор, пока при подставлении её в правую часть уравнения Беллмана ничего не изменится.

То есть, итеративно для каждого состояния будем пересчитывать $v_{\pi}$ по следующей формуле: $v^{k+1}(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a) + \gamma v^{k}(s') \right]$

1. Input: policy $\pi(a|s)$ , discount factor $\gamma$ , small threshold $0 < \gamma \leq 1$
2. Initialize $v_{\pi} = 0$
3. Repeat:
4. For in :
5. $v^{k+1}(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r(s, a) + \gamma v^{k}(s') \right]$
6. $delta = max(delta, |v^{k+1} - v^{k}|)$
7. until $delta < \varepsilon$
8. output v(s)

Этот процесс сходится, потому что оператор Беллмана является сжимающим отображением при $0 <\gamma < 1$ .

6.3. Policy Improvement и action-value function q

Посчитав значения -функции хочется понять как именно улучшить политику.
Давайте будем сравнивать разные политики с помощью -функции:

$\pi \geq \pi' \iff v_\pi(s) \geq v_{\pi'} (s) \quad \forall s$

И пусть $\pi^*$ будет лучшей (оптимальной) политикой.

Мы хотим чтобы чтобы оптимальная политика $\pi^*$ вела нас в состояния с большими наградами. Однако, -функция не зависит от действия.

Тогда давайте выбирать то действие, у которого будет максимальна мгновенная награда + дисконтированная функция состояния:

$\pi'(a|s) = \arg \max_a \mathbb{E}_{s'} [R + \gamma v_{\pi}(s)]$

То есть, мы даем себе выбор первого действия в состоянии .
И для простоты обозначим это новой функцией $q_{\pi}(s, a)$ .

Action-value function q

Action-value function — математическое ожидание суммарной дисконтированной награды , если из состояния мы делаем первое действие (причем не обязательно соответствующее политике $\pi$ ), а дальше играем следуя политике $\pi$ .

$q_\pi(s, a) = \mathbb{E}_\pi \big[ G_t \mid S_t = s, A_t = a \big] =$
Проделаем все тоже самое, что и в state-value

$= \mathbb{E}_\pi \big[ R_t + \gamma G_{t+1} \mid S_t = s, A_t = a \big] =$

$= \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma \mathbb{E}_\pi \big[ G_{t+1} \mid S_{t+1} = s' \big] \Big] =$

Замечаем, что $\mathbb{E}_\pi \big[ G_{t+1} \mid S_{t+1} = s' \big]$ — это $v_\pi(s')$ и обнаруживаем, что можно выписать через :

$= \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

$q_{\pi}(s, a)$ (функция качества всех действий из состояния ) – говорит насколько хорошо выбрать действие в состоянии , если потом следовать политике $\pi$ .

Выше мы выписали -функцию через :

$[2] \quad\quad q_\pi(s, a) = \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

Или так:

$[2] \quad\quad q_\pi(s, a) = \mathbb{E}_{s'} [r + \gamma v_{\pi}(s')]$

Тогда новая политика $\pi'(a|s)$ должна выбирать $\arg\max_{a} q_{\pi}(s, a)$ :

$\pi'(a|s) = \arg\max_{a} q_{\pi}(s, a)$

Более того, улучшение политики через максимизацию -функции приводит к глобально оптимальной политике. Это называется Policy Improvement.

Посчитаем значение q-функции в состоянии s для действий a_0 и a_1:

q(s, a_0) = 1 ( 0 + 0) = 0

q(s, a_1) = 0.1 (1 + 10) + 0.9 (1 - 10) = -7

Заметим, что оптимальной политикой будет закончить игру, выбрав действие a_0 .

Если мы знаем политику $\pi$ , то можем выписать -функцию через :

$v_\pi(s)= \sum_a \pi(a \mid s) \sum_{r, s'} p(r, s' \mid s, a) \big[ r + \gamma v_\pi(s') \big] =$

Заметим, что $\sum_{r, s'} p(r, s' \mid s, a) \big[ r + \gamma v_\pi(s') \big]$ в точности из формулы выше (где выражали через ). Получаем:

$[3] \quad \quad v_\pi(s) = \sum_a \pi(a \mid s) q_\pi(s, a)$

Подставив в формулу [2] вместо $v_\pi (s')$ формулу [3] получим рекуррентное соотношение для :

$[4] \quad \quad q_\pi(s, a) = \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma \sum_{a'} \pi(a' \mid s') q_\pi(s', a') \Big]$

6.4. Уравнения оптимальности Беллмана

Формулы [1] , [2] , [3] , [4] называются уравнениями Беллмана для математического ожидания.

$[1] \quad \quad v_\pi(s) = \sum_a \pi(a \mid s) \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

$[2] \quad\quad q_\pi(s, a) = \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma v_\pi(s') \Big]$

$[3] \quad \quad v_\pi(s) = \sum_a \pi(a \mid s) q_\pi(s, a)$

$[4] \quad \quad q_\pi(s, a) = \sum_{r, s'} p(r, s' \mid s, a) \Big[ r + \gamma \sum_{a'} \pi(a' \mid s') q_\pi(s', a') \Big]$

Данные уравнения являются ключевым результатом для построения всех последующих RL-алгоритмов.

Если $\pi_*$ — лучшая (оптимальная) политика.
Оптимальная state-value функция: $v_∗(s) = \max v_\pi(s)$ .
Оптимальная action-value функция : $q_∗(s,a)=max_\pi a_\pi(s,a)$ .

В любом конечном MDP существует хотя бы одна оптимальная политика.

Уравнение оптимальности Беллмана для — это то же уравнение Беллмана для мат. ожидания, только с максимумом по действиям (сравниваем действия между собой по будущей награде).

Уравнение оптимальности Беллмана для v

$[5] \quad \quad v_{*}(s) = \color{red}{\max_{a}} \mathbb{E}_{s'}[r + \gamma v_{*}(s')]$

Уравнение оптимальности Беллмана для отличается от уравнения Беллмана для мат. ожидания тем, что мы берем максимум по политике:

Уравнение оптимальности Беллмана для q

$[6] \quad \quad q_{*}(s, a) = \mathbb{E}_{s'} \left[ R + \gamma \color{red}{\max_{a'}} q_{*}(s', \color{red}{a'}) \right]$

Aналогично определим связь между v_* и q_* :

$[7] \quad \quad q_{*}(s, a) = \mathbb{E}_{s'} \left[ R + \gamma v_{*}(s') \right]$ $[8] \quad \quad v_{*}(s) = \max_{a} q_{*} (s, a)$

7. Generalized Policy Iteration

Policy Iteration — это алгоритм, который ищет оптимальную политику $\pi_*$ с помощью итеративного чередования двух шагов: оценки политики (policy evaluation) и улучшения политики (policy improvement).

policy = Initialize_policy()
while not optimal:
  # оцениваем политику (матрично или итеративно)
  v = Evaluate_Policy(policy)  
  # улучшим политику, взяв действие как argmax
  new_policy = imprive_policy(v)
  # проверяем, сошлись ли к глобально оптимальной политике
  is_optimal = [new_polixy == policy] 
  policy = new_policy

Подставим конкретные способы оценки и обновления политики:

В качестве оценки политикиEvaluate_Policy(policy) возьмем метод простой итерации: для всех состояний $s \in S$ будем применять уравнение Беллмана к , пока не сойдемся.

for some iterations:
  for s in S:
     v(s) = evaluate_policy_in_state(s, policy)

В качестве улучшения политики imprive_policy(v) возьмём жадное обновление по argmax: для всех состояний $s \in S$ будем выбирать действие, которое максимизирует ожидаемое значение награды $\arg \max_{a} q(s,a)$ .

for s in S:
  policy(s) = improve_polic_in_statr(s, v)

На практике можно улучшать политику не во всех состояниях, а в некоторых на каждом шаге. Или, можно оценивать политику только частично (ограничив число итераций), не доводя до сходимости. Тем не менее, даже при таком чередовании частичных шагов оценки и улучшения, алгоритм всё равно гарантированно сойдётся. Такой подход называется обобщённой итерацией по политике (Generalized Policy Iteration, GPI).

Из GPI вытекают два важных частных случая:

Policy Iteration (итерация по политике) — когда оценка политики проводится до сходимости, а затем выполняется полное жадное улучшение политики (его рассмотрели выше).
Value Iteration (итерация по значениям) — когда выполняется всего один шаг оценки (частичное обновление) и сразу жадное улучшение политики.

for 1 iterations:
  for s in S:
     v(s) = evaluate_policy_in_state(s, policy)

for s in S:
  policy(s) = improve_polic_in_statr(s, v)

Выкинем for по iterations и объединим в один цикл по S:

for s in S:
  v(s) = evaluate_policy_in_state(s, policy)
  policy(s) = improve_policy_in_statr(s, v)

Распишем шаг Policy Evaluation:
$v(s) = \mathbb{E}_{a} \mathbb{E}_{s'} \left[ r + \gamma v(s') \right]$

Шаг improve policy:
$\pi(s) = \arg \max_a \mathbb{E}_{s'} \left[ r + \gamma v(s') \right]$

Подставив одну операцию в другую и получим в точности уравнение Беллмана для оптимальных политик [5] : $v(s) = \max_a \mathbb{E}_{s'} \left[ r + \gamma v(s') \right]$

Данный алгоритм – это метод простой итерации для оптимального уравнения Беллмана. Он будет сходиться, поскольку оптимальные уравнения Беллмана тоже являются операторами сжатия.

1. Initialize $V^{(0)}(s)=0$ , for all
2. For $i=0, 1, 2, \dots$
3. $\quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] \text{,} \quad \forall s$

Ноутбук потыкать (семинар с курса Practical RL). Надеюсь что все верно (• ◡•)

Резюмируя

RL(обучение с подкреплением) – обучение методом проб и ошибок.
Главное отличие от обучения с учителем – не требует размеченной выборки и дифференцируемой лосс функции.

Reward (награда) – скалярная величина, которая предоставляет какой-то «сигнал» для обучения (хорошо/плохо). Задача агента – максимизировать сумму наград.
Правильно выбрать функцию награды не так просто: с одной стороны надо награждать агента только за достижение цели, с другой награды не должны быть слишком редкими.
Для задач с бесконечными эпизодами добавили параметр дисконтирования $\gamma$ чтобы учитывать лишь часть будущих наград, а не накапливать бесконечную сумму.

State-value function – функция, показывающая насколько в текущем состоянии все хорошо. С помощью Policy Evaluation оцениваем v(s) для каждого состояния . Есть два способа: решить СЛАУ (matrix way) или с помощью методы простых итерций (fixed-point iteration).

Action-value function – функция, показывающая насколько хорошо в текущем состоянии совершить действие . Policy Improvement помогает выбрать оптимальное действие в состоянии (политику) как $\arg \max_a q(s, a_i)$ .

Generalized Policy Iteration – алгоритм поиска оптимальной стратегии путем чередования Policy Evaluation и Policy Improvement. Существует две крайности данного алгоритма: Policy Iteration и Value Iteration.

Policy Iteration – когда Policy Evaluation считается до сходимости.
1. Инициализируем $\pi_0$ (случайно или равновероятно)
2. For $n=0, 1, 2, \dots$
3. Считаем state-value функцию $V^{\pi_{n}}$ (методом фиксированной точки)
4. Используем $V^{\pi_{n}}$ для подсчета state-action-value функции $Q^{\pi_{n}}$
5. Ищем новую политику $Q^{\pi_{n}} = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$

Value Iteration – когда выполняется всего один шаг Policy Evaluation и сразу Policy Improvement.
1. Инициализируем $V^{(0)}(s)=0$ (или еще чем-то)
2. For $i=0, 1, 2, \dots$
3. $\quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] \text{,} \quad \forall s$
4. Ищем политику как $\pi(s) = \operatorname*{argmax}_a Q(s,a)$ .

Рассуждения выше справедливы для относительно простых задач, где известна матрица переходов P(s',r|s,a) из одного состояния в другое при каждом действии. Такие задачи еще называют Model-based RL.

На данный момент готовлю вторую часть про задачи, когда нам не известна модель среды Model-free RL.

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"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.10.25 01:12 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.10.25 19:53 Tonerdomark

A crook swiped my Dogecoin. It ruined my whole world. Then Mr. Sylvester showed up. He fixed it all. He pulled back €211,000 for me. Not one cent missing from my profits. His steady cool and sharp tech know-how won back my trust. I got my money smooth and sound. After endless worry, relief hit me hard. I trusted him completely. Lost cash to a scam? Hit him up now at { yt7cracker@gmail . com }. His aid turned my life around. WhatsApp at +1 512 577 7957.
12.10.25 21:36 blessing

Writing this review is a joy. Marie has provided excellent service ever since I started working with her in early 2018. I was worried I wouldn't be able to get my coins back after they were stolen by hackers. I had no idea where to begin, therefore it was a nightmare for me. However, things became easier for me after my friend sent me to [email protected] and +1 7127594675 on WhatsApp. I'm happy that she was able to retrieve my bitcoin so that I could resume trading.
13.10.25 01:11 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.10.25 01:11 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.10.25 01:15 tyleradams

Hi. Please be wise, do not make the same mistake I had made in the past, I was a victim of bitcoin scam, I saw a glamorous review showering praises and marketing an investment firm, I reached out to them on what their contracts are, and I invested $28,000, which I was promised to get my first 15% profit in weeks, when it’s time to get my profits, I got to know the company was bogus, they kept asking me to invest more and I ran out of patience then requested to have my money back, they refused to answer nor refund my funds, not until a friend of mine introduced me to the NVIDIA TECH HACKERS, so I reached out and after tabling my complaints, they were swift to action and within 36 hours I got back my funds with the due profit. I couldn’t contain the joy in me. I urge you guys to reach out to NVIDIA TECH HACKERS on their email: [email protected]
14.10.25 08:46 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.10.25 08:46 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.10.25 08:46 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.10.25 18:07 crypto

Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.
15.10.25 21:52 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.10.25 21:52 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.25 20:17 tyleradams

As time passes, there are an increasing number of frauds involving Bitcoin and other cryptocurrencies. Although there are many individuals who advertise recovering money online, people should use caution in dealing, especially when money is involved. You can trust NVIDIA TECH HACKERS [[email protected]], I promise. They are the top internet recovery company, and as their names indicate, your money is reclaimed as soon as feasible. My bitcoin was successfully retrieved in large part thanks to NVIDIA TECH HACKERS. Ensure that you get top-notch service; NVIDIA TECH HACKERS provides evidence of its work; and payment is only made when the service has been completed to your satisfaction. Reach them via email: [email protected] on google mail
17.10.25 20:20 lindseyvonn

Have you gotten yourself involved in a cryptocurrency scam or any scam at all? If yes, know that you are not alone, there are a lot of people in this same situation. I'm a Health Worker and was a victim of a cryptocurrency scam that cost me a lot of money. This happened a few weeks ago, there’s only one solution which is to talk to the right people, if you don’t do this you will end up being really depressed. I was really devastated until went on LinkedIn one evening after my work hours and i saw lots of reviews popped up on my feed about [email protected], I sent an email to the team who came highly recommended - [email protected] I started seeing some hope for myself from the moment I sent them an email. The good part is they made the entire process stress free for me, i literally sat and waited for them to finish and I received what I lost in my wallet
17.10.25 20:22 richardcharles

I would recommend NVIDIA TECH HACKERS to anyone that needs this service. I decided to get into crypto investment and I ended up getting my crypto lost to an investor late last year. The guy who was supposed to be managing my account turned out to be a scammer all along. I invested 56,000 USD and at first, my reading and profit margins were looking good. I started getting worried when I couldn’t make withdrawals and realized that I’ve been scammed. I came across some of the testimonials that people said about NVIDIA TECH HACKERS and how helpful he has been in recovering their funds. I immediately contacted him in his mail at [email protected] so I can get his assistance. One week into the recovery process the funds were traced and recovered back from the scammer. I can't appreciate him enough for his professionalism.
17.10.25 20:23 stevekalfman

If you need a hacker for scam crypto recovery or mobile spy access remotely kindly reach out to [email protected] for quick response, I hired this hacker and he did a nice job. before NVIDIA TECH HACKERS, I met with different hacker's online which turns out to be scam, this NVIDIA TECH HACKERS case was different and he is the trusted hacker I can vote and refer.
17.10.25 21:42 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.25 21:42 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.25 21:42 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.10.25 08:39 debby131

Given how swiftly the cryptocurrency market moves, losing USDT may be a terrifying and upsetting experience. Whether you experienced a technical problem, a transaction error, or were the victim of fraud, it is important to understand the potential recovery routes. Marie can assist you in determining the specific actions you can take to attempt to regain your lost USDT when you need guidance and clarification. You can reach her via email at [email protected] and WhatsApp at +1 7127594675.
21.10.25 11:45 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.10.25 11:45 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.10.25 04:48 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
22.10.25 07:36 donnacollier

HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM Hello everyone l’m by name Donna collier I live in urbandale 3 weeks ago was the darkest days of my life, i invested my hard earned money the sum of $123,000 into a crypto currency platform I was introduced to by a friend I met online everything happen so fast I was promised 300% of return of investment when it was time for me to cash out my investment and profit the platform was down I was so diversitated confused and tried to end it all then I came across upswing Ai a renowned expert in crypto currency and digital assets recovery at first it seem impossible after taking up my case within the the next 48 hours they where able to track down those fraud stars and recover my money I can’t recommend them enough to any one facing likewise change I will recommend you contact upswing Ai on Contact Details: WhatsApp +,1,2,0,2,8,1,0,1,4,0,7 E m a i l @Upswing-ai.com Website https: // u psw ing-ai. com/ platform /
22.10.25 11:59 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.10.25 11:59 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.10.25 16:31 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
23.10.25 01:52 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.10.25 01:52 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.10.25 15:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
23.10.25 21:43 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.10.25 21:43 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.10.25 06:08 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
24.10.25 06:40 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.10.25 06:40 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.10.25 06:54 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
24.10.25 18:18 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.10.25 18:18 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.10.25 00:49 tyleradams

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25.10.25 00:50 stevekalfman

If you ever need hacking services, look no further. I found myself in a difficult situation after losing almost $510,000 USD in bitcoin. I was distraught and had no hope of survival because i lost my life savings to this scam, I had no chance of recovering my investment. Until i came across an article on google about ([email protected]). A real-life recovery expert, everything changed completely after contacting him and explaining my ordeal to him and he quickly stepped in and assisted me in recovering 95% of my lost funds. They guarantee their clients and i got the highest level of happiness their services are highly recommended. so I’m putting this here for anyone who require their services too" Email: [email protected]
25.10.25 05:05 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
25.10.25 10:13 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.10.25 10:13 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.10.25 01:03 Christopherbelle

A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.
26.10.25 18:09 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 17:08 raymondgonzales

Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number +18737715701 Good Day.
27.10.25 17:20 fatimanorth

The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.
28.10.25 00:55 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.10.25 00:55 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.10.25 03:43 Christopherbelle

A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.
29.10.25 10:56 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.10.25 10:56 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.10.25 09:49 Christopherbelle

I suffered a huge money blow when $80,000 slipped away in a bogus crypto plot. It all looked great at first. Then I went to pull out my gains, and poof—my account was gone. I kept telling the cops about it, but they did zip. I felt shattered and lost. That's when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed clear steps, sharp know-how, and real drive to fix it. They tracked my missing cash step by step and pushed hard till they got it back. I swear, I figured it was a lost cause. Their straight-up work and trust brought back my calm. If a scam stole your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
30.10.25 12:03 elizabethrush89

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31.10.25 13:25 Lillian Lizzy

THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.
31.10.25 13:25 Lillian Lizzy

THANKS TO THE SERVICES OF THE HACK ANGELS // FOR HELPING ME RECOVER MY USDT AND BTC I lost almost $698,000 in a bitcoin investment scam a few months ago. I was devastated and depressed, and I didn't know what to do. When I saw a favorable review of THE HACK ANGELS RECOVERY EXPERT. I decided to contact them and voice my concerns. God is so good that I am a living testament to the fact that there are still legitimate recovery hackers out there. I will confidently recommend THE HACK ANGELS RECOVERY EXPERT to everyone I meet. I will suggest them to anyone who falls victim to any kind of online scam by using the information below. web: https://thehackangels.com Mail Box; [email protected] WhatsApp; +1(520)-200,2320 If you're in London, you can even visit them in person at their office located at 45-46 Red Lion Street, London WC1R 4PF, UK.
01.11.25 03:27 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.11.25 03:27 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.11.25 15:47 kattygates

Hack West Credit Repair is truly in the business of helping people understand credit, how credit works and most importantly they truly care that you understand your next steps to securing a better tomorrow for you and your family. I am grateful that the owner West has taken time out of his evening with his family to get me enrolled and he immediately got the ball rolling in helping me get items deleted from my credit reports. In the few months I’ve been with HACK WEST, 15 of the 17 negative items have been deleted and 250 points have been added to my point. If you want great results, I suggest you use [email protected].
01.11.25 15:49 kattygates

I met an individual on an international dating app, Bumpy. After talking for a few months, the individual encouraged me to start investing on crypto asset trading platform, btc01.org. I started trading and believed I was making profit until I tried to withdraw some of my money, I was asked to pay extra for tax which I did and they kept asking then I knew I have been scammed, I had to contact HACKWEST AT WRITEME DOT COM who then helped to recover the money, the total money I invest is $198,000 in bitcoin. The website is no longer operational. If anyone is in a similar issue, you can as well contact HACK WEST. They also fixed my credit report.
02.11.25 10:55 Christopherbelle

I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
02.11.25 10:56 Christopherbelle

I suffered a crushing blow when $45,000 slipped away in a phony crypto scam. It all looked great at first. But when I went to pull out my gains, my account just vanished. I called the cops over and over. Still, no luck. I felt shattered and lost. That’s when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed real openness, sharp skills, and a drive to fix it. They tracked my missing money step by step. And they pushed hard until they got it back. I honestly didn’t believe it could happen. Their straight-up approach and solid work brought back my calm. If a scam took your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
02.11.25 15:23 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
02.11.25 15:23 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.11.25 04:59 Christopherbelle

How to Recover Bitcoin Stolen by a Scammer I dropped £75,000 into a fake crypto scheme. Everything seemed perfect right from the start. But when I tried to cash out my profits, the whole account disappeared. I rang the police time and again. They offered no help at all. I felt broken and alone. Then I found Sylvester Bryant Intelligence. My luck changed in no time. They spoke plainly, worked smart, and focused on my case. They followed the trail of my lost cash bit by bit. They fought until they recovered it all. I never thought it was possible. Their honest approach and expertise restored my peace. If a scam has stolen your crypto, contact them now. [email protected] | WhatsApp: +1 512 577 7957 or +44 7428 662701
04.11.25 09:30 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.11.25 09:30 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.11.25 02:43 jordan_11

I made a mistake of not researching about their their investment firm(Binary option), it had a lot of promises which made me fall for all their fake promises , after trying to get my withdrawal out from there, I started having a lot of difficulties. Then I contacted their customer support, they only replied a week after and strangely wanted me to make more deposits just to enable my withdrawal, so i started my research of how I could report this treacherous company to the necessary authorities and also maybe i could get back my investment, The only people that were willing to help me out was Treqora Intel, their customer support replied so fast and immediately directed me to their investigative team which took my up my case and started the tracing and reclaim process with swift, after a week i got an email from Treqora Intel stating that a partial amount had been reclaimed, I was so grateful about their help , then I was asked to decide if I wanted a Partial deposit or wanted all my investment reclaimed and sent to me at once, But I was so desperate at the time so I asked that my partial reclaimed ETH be sent to me first , So the deposit took about few minutes before i got it in my wallet and withdrew it. Then my remaining investment took 2 weeks to get back according to their customer support at Treqora Intel. Immediately They got it, I was contacted again Via email that my reclaimed had been fully reclaimed, so grateful till this day to Treqora Intel for taking their time to help me out with what could have been a very depressing moment to me. And yes no upfront payment until the reclaim has been completed and you've been paid fully. Email:support@treqora. com 📱 WhatsApp: ‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬ ‬‬ 🌐 Website: Treqora. com.
05.11.25 02:44 jordan_11

Crypto Recovery Services _Hire Treqora Intel
05.11.25 02:48 jordan_11

Legitimate Crypto Recovery Companies-CONSULT TREQORA INTEL. After falling victim to a crypt0currency scam group, I lost $35,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to rec0vermy stolen funds and I came across a lot of testimonials online about TREQORA INTEL , an agent who helps in rec0ver of lost bitc0in funds, I contacted TREQORA INTEL , and with their expertise, they successfully traced and rec0vered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and rec0very protocols. They are trusted and very reliable with a 100% successful rate record Rec0very bitc0in, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypt0. Email:support@treqora. com Whats_App: ‪‪‪‪‪+1 (7 7 3 ) 9 7 7 - 7 8 7 7‬ ‬‬ ‬‬, Website: Treqora dot com.
05.11.25 16:20 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.11.25 16:21 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1