diff --git a/labml_nn/rl/dqn/__init__.py b/labml_nn/rl/dqn/__init__.py
index e69de29b..b23f9d54 100644
--- a/labml_nn/rl/dqn/__init__.py
+++ b/labml_nn/rl/dqn/__init__.py
@@ -0,0 +1,50 @@
+"""
+This is a Deep Q Learning implementation with:
+* Double Q Network
+* Dueling Network
+* Prioritized Replay
+"""
+
+from typing import Tuple
+
+import torch
+
+from labml import tracker
+from labml_helpers.module import Module
+from labml_nn.rl.dqn.replay_buffer import ReplayBuffer
+
+
+class QFuncLoss(Module):
+ def __init__(self, gamma: float):
+ super().__init__()
+ self.gamma = gamma
+
+ def __call__(self, q: torch.Tensor,
+ action: torch.Tensor,
+ double_q: torch.Tensor,
+ target_q: torch.Tensor,
+ done: torch.Tensor,
+ reward: torch.Tensor,
+ weights: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
+ q_sampled_action = q.gather(-1, action.to(torch.long).unsqueeze(-1)).squeeze(-1)
+ tracker.add('q_sampled_action', q_sampled_action)
+
+ with torch.no_grad():
+ best_next_action = torch.argmax(double_q, -1)
+ best_next_q_value = target_q.gather(-1, best_next_action.unsqueeze(-1)).squeeze(-1)
+
+ best_next_q_value *= (1 - done)
+
+ q_update = reward + self.gamma * best_next_q_value
+ tracker.add('q_update', q_update)
+
+ td_error = q_sampled_action - q_update
+ tracker.add('td_error', td_error)
+
+ # Huber loss
+ losses = torch.nn.functional.smooth_l1_loss(q_sampled_action, q_update, reduction='none')
+ loss = torch.mean(weights * losses)
+ tracker.add('loss', loss)
+
+ return td_error, loss
+
diff --git a/labml_nn/rl/dqn/experiment.py b/labml_nn/rl/dqn/experiment.py
new file mode 100644
index 00000000..817f7cf0
--- /dev/null
+++ b/labml_nn/rl/dqn/experiment.py
@@ -0,0 +1,385 @@
+"""
+\(
+ \def\hl1#1{{\color{orange}{#1}}}
+ \def\blue#1{{\color{cyan}{#1}}}
+ \def\green#1{{\color{yellowgreen}{#1}}}
+\)
+"""
+
+import numpy as np
+import torch
+from torch import nn
+
+from labml import tracker, experiment, logger, monit
+from labml_helpers.module import Module
+from labml_helpers.schedule import Piecewise
+from labml_nn.rl.dqn import QFuncLoss
+from labml_nn.rl.dqn.replay_buffer import ReplayBuffer
+from labml_nn.rl.game import Worker
+
+if torch.cuda.is_available():
+ device = torch.device("cuda:0")
+else:
+ device = torch.device("cpu")
+
+
+class Model(Module):
+ """
+ ## Neural Network Model for $Q$ Values
+
+ #### Dueling Network ⚔️
+ We are using a [dueling network](https://arxiv.org/abs/1511.06581)
+ to calculate Q-values.
+ Intuition behind dueling network architure is that in most states
+ the action doesn't matter,
+ and in some states the action is significant. Dueling network allows
+ this to be represented very well.
+
+ \begin{align}
+ Q^\pi(s,a) &= V^\pi(s) + A^\pi(s, a)
+ \\
+ \mathop{\mathbb{E}}_{a \sim \pi(s)}
+ \Big[
+ A^\pi(s, a)
+ \Big]
+ &= 0
+ \end{align}
+
+ So we create two networks for $V$ and $A$ and get $Q$ from them.
+ $$
+ Q(s, a) = V(s) +
+ \Big(
+ A(s, a) - \frac{1}{|\mathcal{A}|} \sum_{a' \in \mathcal{A}} A(s, a')
+ \Big)
+ $$
+ We share the initial layers of the $V$ and $A$ networks.
+ """
+
+ def __init__(self):
+ """
+ ### Initialize
+
+ We need `scope` because we need multiple copies of variables
+ for target network and training network.
+ """
+
+ super().__init__()
+ self.conv = nn.Sequential(
+ # The first convolution layer takes a
+ # 84x84 frame and produces a 20x20 frame
+ nn.Conv2d(in_channels=4, out_channels=32, kernel_size=8, stride=4),
+ nn.ReLU(),
+
+ # The second convolution layer takes a
+ # 20x20 frame and produces a 9x9 frame
+ nn.Conv2d(in_channels=32, out_channels=64, kernel_size=4, stride=2),
+ nn.ReLU(),
+
+ # The third convolution layer takes a
+ # 9x9 frame and produces a 7x7 frame
+ nn.Conv2d(in_channels=64, out_channels=64, kernel_size=3, stride=1),
+ nn.ReLU(),
+ )
+
+ # A fully connected layer takes the flattened
+ # frame from third convolution layer, and outputs
+ # 512 features
+ self.lin = nn.Linear(in_features=7 * 7 * 64, out_features=512)
+
+ self.state_score = nn.Sequential(
+ nn.Linear(in_features=512, out_features=256),
+ nn.ReLU(),
+ nn.Linear(in_features=256, out_features=1),
+ )
+ self.action_score = nn.Sequential(
+ nn.Linear(in_features=512, out_features=256),
+ nn.ReLU(),
+ nn.Linear(in_features=256, out_features=4),
+ )
+
+ #
+ self.activation = nn.ReLU()
+
+ def __call__(self, obs: torch.Tensor):
+ h = self.conv(obs)
+ h = h.reshape((-1, 7 * 7 * 64))
+
+ h = self.activation(self.lin(h))
+
+ action_score = self.action_score(h)
+ state_score = self.state_score(h)
+
+ # $Q(s, a) =V(s) + \Big(A(s, a) - \frac{1}{|\mathcal{A}|} \sum_{a' \in \mathcal{A}} A(s, a')\Big)$
+ action_score_centered = action_score - action_score.mean(dim=-1, keepdim=True)
+ q = state_score + action_score_centered
+
+ return q
+
+
+def obs_to_torch(obs: np.ndarray) -> torch.Tensor:
+ """Scale observations from `[0, 255]` to `[0, 1]`"""
+ return torch.tensor(obs, dtype=torch.float32, device=device) / 255.
+
+
+class Main(object):
+ """
+ ## Main class
+ This class runs the training loop.
+ It initializes TensorFlow, handles logging and monitoring,
+ and runs workers as multiple processes.
+ """
+
+ def __init__(self):
+ """
+ ### Initialize
+ """
+
+ # #### Configurations
+
+ # number of workers
+ self.n_workers = 8
+ # steps sampled on each update
+ self.worker_steps = 4
+ # number of training iterations
+ self.train_epochs = 8
+
+ # number of updates
+ self.updates = 1_000_000
+ # size of mini batch for training
+ self.mini_batch_size = 32
+
+ # exploration as a function of time step
+ self.exploration_coefficient = Piecewise(
+ [
+ (0, 1.0),
+ (25_000, 0.1),
+ (self.updates / 2, 0.01)
+ ], outside_value=0.01)
+
+ # update target network every 250 update
+ self.update_target_model = 250
+
+ # $\beta$ for replay buffer as a function of time steps
+ self.prioritized_replay_beta = Piecewise(
+ [
+ (0, 0.4),
+ (self.updates, 1)
+ ], outside_value=1)
+
+ # replay buffer
+ self.replay_buffer = ReplayBuffer(2 ** 14, 0.6)
+
+ self.model = Model().to(device)
+ self.target_model = Model().to(device)
+
+ # last observation for each worker
+ # create workers
+ self.workers = [Worker(47 + i) for i in range(self.n_workers)]
+
+ # initialize tensors for observations
+ self.obs = np.zeros((self.n_workers, 4, 84, 84), dtype=np.uint8)
+ for worker in self.workers:
+ worker.child.send(("reset", None))
+ for i, worker in enumerate(self.workers):
+ self.obs[i] = worker.child.recv()
+
+ self.loss_func = QFuncLoss(0.99)
+ # optimizer
+ self.optimizer = torch.optim.Adam(self.model.parameters(), lr=2.5e-4)
+
+ def _sample_action(self, q_value: torch.Tensor, exploration_coefficient: float):
+ """
+ #### $\epsilon$-greedy Sampling
+ When sampling actions we use a $\epsilon$-greedy strategy, where we
+ take a greedy action with probabiliy $1 - \epsilon$ and
+ take a random action with probability $\epsilon$.
+ We refer to $\epsilon$ as *exploration*.
+ """
+
+ with torch.no_grad():
+ greedy_action = torch.argmax(q_value, dim=-1)
+ random_action = torch.randint(q_value.shape[-1], greedy_action.shape, device=q_value.device)
+
+ is_choose_rand = torch.rand(greedy_action.shape, device=q_value.device) < exploration_coefficient
+
+ return torch.where(is_choose_rand, random_action, greedy_action).cpu().numpy()
+
+ def sample(self, exploration_coefficient: float):
+ """### Sample data"""
+
+ with torch.no_grad():
+ # sample `SAMPLE_STEPS`
+ for t in range(self.worker_steps):
+ # sample actions
+ q_value = self.model(obs_to_torch(self.obs))
+ actions = self._sample_action(q_value, exploration_coefficient)
+
+ # run sampled actions on each worker
+ for w, worker in enumerate(self.workers):
+ worker.child.send(("step", actions[w]))
+
+ # collect information from each worker
+ for w, worker in enumerate(self.workers):
+ # get results after executing the actions
+ next_obs, reward, done, info = worker.child.recv()
+
+ # add transition to replay buffer
+ self.replay_buffer.add(self.obs[w], actions[w], reward, next_obs, done)
+
+ # update episode information
+ # collect episode info, which is available if an episode finished;
+ # this includes total reward and length of the episode -
+ # look at `Game` to see how it works.
+ # We also add a game frame to it for monitoring.
+ if info:
+ tracker.add('reward', info['reward'])
+ tracker.add('length', info['length'])
+
+ # update current observation
+ self.obs[w] = next_obs
+
+ def train(self, beta: float):
+ """
+ ### Train the model
+
+ We want to find optimal action-value function.
+
+ \begin{align}
+ Q^*(s,a) &= \max_\pi \mathbb{E} \Big[
+ r_t + \gamma r_{t + 1} + \gamma^2 r_{t + 2} + ... | s_t = s, a_t = a, \pi
+ \Big]
+ \\
+ Q^*(s,a) &= \mathop{\mathbb{E}}_{s' \sim \large{\varepsilon}} \Big[
+ r + \gamma \max_{a'} Q^* (s', a') | s, a
+ \Big]
+ \end{align}
+
+ #### Target network 🎯
+ In order to improve stability we use experience replay that randomly sample
+ from previous experience $U(D)$. We also use a Q network
+ with a separate set of paramters $\hl1{\theta_i^{-}}$ to calculate the target.
+ $\hl1{\theta_i^{-}}$ is updated periodically.
+ This is according to the [paper by DeepMind](https://deepmind.com/research/dqn/).
+
+ So the loss function is,
+ $$
+ \mathcal{L}_i(\theta_i) = \mathop{\mathbb{E}}_{(s,a,r,s') \sim U(D)}
+ \bigg[
+ \Big(
+ r + \gamma \max_{a'} Q(s', a'; \hl1{\theta_i^{-}}) - Q(s,a;\theta_i)
+ \Big) ^ 2
+ \bigg]
+ $$
+
+ #### Double $Q$-Learning
+ The max operator in the above calculation uses same network for both
+ selecting the best action and for evaluating the value.
+ That is,
+ $$
+ \max_{a'} Q(s', a'; \theta) = \blue{Q}
+ \Big(
+ s', \mathop{\operatorname{argmax}}_{a'}
+ \blue{Q}(s', a'; \blue{\theta}); \blue{\theta}
+ \Big)
+ $$
+ We use [double Q-learning](https://arxiv.org/abs/1509.06461), where
+ the $\operatorname{argmax}$ is taken from $\theta_i$ and
+ the value is taken from $\theta_i^{-}$.
+
+ And the loss function becomes,
+ \begin{align}
+ \mathcal{L}_i(\theta_i) = \mathop{\mathbb{E}}_{(s,a,r,s') \sim U(D)}
+ \Bigg[
+ \bigg(
+ &r + \gamma \blue{Q}
+ \Big(
+ s',
+ \mathop{\operatorname{argmax}}_{a'}
+ \green{Q}(s', a'; \green{\theta_i}); \blue{\theta_i^{-}}
+ \Big)
+ \\
+ - &Q(s,a;\theta_i)
+ \bigg) ^ 2
+ \Bigg]
+ \end{align}
+ """
+
+ for _ in range(self.train_epochs):
+ # sample from priority replay buffer
+ samples = self.replay_buffer.sample(self.mini_batch_size, beta)
+ # train network
+ q_value = self.model(obs_to_torch(samples['obs']))
+
+ with torch.no_grad():
+ double_q_value = self.model(obs_to_torch(samples['next_obs']))
+ target_q_value = self.target_model(obs_to_torch(samples['next_obs']))
+
+ td_errors, loss = self.loss_func(q_value,
+ q_value.new_tensor(samples['action']),
+ double_q_value, target_q_value,
+ q_value.new_tensor(samples['done']),
+ q_value.new_tensor(samples['reward']),
+ q_value.new_tensor(samples['weights']))
+
+ # $p_i = |\delta_i| + \epsilon$
+ new_priorities = np.abs(td_errors.cpu().numpy()) + 1e-6
+ # update replay buffer
+ self.replay_buffer.update_priorities(samples['indexes'], new_priorities)
+
+ # compute gradients
+ self.optimizer.zero_grad()
+ loss.backward()
+ torch.nn.utils.clip_grad_norm_(self.model.parameters(), max_norm=0.5)
+ self.optimizer.step()
+
+ def run_training_loop(self):
+ """
+ ### Run training loop
+ """
+
+ # copy to target network initially
+ self.target_model.load_state_dict(self.model.state_dict())
+
+ # last 100 episode information
+ tracker.set_queue('reward', 100, True)
+ tracker.set_queue('length', 100, True)
+
+ for update in monit.loop(self.updates):
+ # $\epsilon$, exploration fraction
+ exploration = self.exploration_coefficient(update)
+ tracker.add('exploration', exploration)
+ # $\beta$ for priority replay
+ beta = self.prioritized_replay_beta(update)
+ tracker.add('beta', beta)
+
+ # sample with current policy
+ self.sample(exploration)
+
+ if self.replay_buffer.is_full():
+ # train the model
+ self.train(beta)
+
+ # periodically update target network
+ if update % self.update_target_model == 0:
+ self.target_model.load_state_dict(self.model.state_dict())
+
+ tracker.save()
+ if (update + 1) % 1_000 == 0:
+ logger.log()
+
+ def destroy(self):
+ """
+ ### Destroy
+ Stop the workers
+ """
+ for worker in self.workers:
+ worker.child.send(("close", None))
+
+
+# ## Run it
+if __name__ == "__main__":
+ experiment.create(name='dqn')
+ m = Main()
+ with experiment.start():
+ m.run_training_loop()
+ m.destroy()
diff --git a/labml_nn/rl/dqn/replay_buffer.py b/labml_nn/rl/dqn/replay_buffer.py
new file mode 100644
index 00000000..48d79f44
--- /dev/null
+++ b/labml_nn/rl/dqn/replay_buffer.py
@@ -0,0 +1,236 @@
+import numpy as np
+import random
+
+
+class ReplayBuffer:
+ """
+ ## Buffer for Prioritized Experience Replay
+ [Prioritized experience replay](https://arxiv.org/abs/1511.05952)
+ samples important transitions more frequently.
+ The transitions are prioritized by the Temporal Difference error.
+
+ We sample transition $i$ with probability,
+ $$P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$$
+ where $\alpha$ is a hyper-parameter that determines how much
+ prioritization is used, with $\alpha = 0$ corresponding to uniform case.
+
+ We use proportional prioritization $p_i = |\delta_i| + \epsilon$ where
+ $\delta_i$ is the temporal difference for transition $i$.
+
+ We correct the bias introduced by prioritized replay by
+ importance-sampling (IS) weights
+ $$w_i = \bigg(\frac{1}{N} \frac{1}{P(i)}\bigg)^\beta$$
+ that fully compensates for when $\beta = 1$.
+ We normalize weights by $1/\max_i w_i$ for stability.
+ Unbiased nature is most important towards the convergence at end of training.
+ Therefore we increase $\beta$ towards end of training.
+
+ ### Binary Segment Trees
+ We use binary segment trees to efficiently calculate
+ $\sum_k^i p_k^\alpha$, the cumulative probability,
+ which is needed to sample.
+ We also use a binary segment tree to find $\min p_i^\alpha$,
+ which is needed for $1/\max_i w_i$.
+ We can also use a min-heap for this.
+
+ This is how a binary segment tree works for sum;
+ it is similar for minimum.
+ Let $x_i$ be the list of $N$ values we want to represent.
+ Let $b_{i,j}$ be the $j^{\mathop{th}}$ node of the $i^{\mathop{th}}$ row
+ in the binary tree.
+ That is two children of node $b_{i,j}$ are $b_{i+1,2j}$ and $b_{i+1,2j + 1}$.
+
+ The leaf nodes on row $D = \left\lceil {1 + \log_2 N} \right\rceil$
+ will have values of $x$.
+ Every node keeps the sum of the two child nodes.
+ So the root node keeps the sum of the entire array of values.
+ The two children of the root node keep
+ the sum of the first half of the array and
+ the sum of the second half of the array, and so on.
+
+ $$b_{i,j} = \sum_{k = (j -1) * 2^{D - i} + 1}^{j * 2^{D - i}} x_k$$
+
+ Number of nodes in row $i$,
+ $$N_i = \left\lceil{\frac{N}{D - i + i}} \right\rceil$$
+ This is equal to the sum of nodes in all rows above $i$.
+ So we can use a single array $a$ to store the tree, where,
+ $$b_{i,j} = a_{N_1 + j}$$
+
+ Then child nodes of $a_i$ are $a_{2i}$ and $a_{2i + 1}$.
+ That is,
+ $$a_i = a_{2i} + a_{2i + 1}$$
+
+ This way of maintaining binary trees is very easy to program.
+ *Note that we are indexing from 1*.
+ """
+
+ def __init__(self, capacity, alpha):
+ """
+ ### Initialize
+ """
+ # we use a power of 2 for capacity to make it easy to debug
+ self.capacity = capacity
+ # we refill the queue once it reaches capacity
+ self.next_idx = 0
+ # $\alpha$
+ self.alpha = alpha
+
+ # maintain segment binary trees to take sum and find minimum over a range
+ self.priority_sum = [0 for _ in range(2 * self.capacity)]
+ self.priority_min = [float('inf') for _ in range(2 * self.capacity)]
+
+ # current max priority, $p$, to be assigned to new transitions
+ self.max_priority = 1.
+
+ # arrays for buffer
+ self.data = {
+ 'obs': np.zeros(shape=(capacity, 4, 84, 84), dtype=np.uint8),
+ 'action': np.zeros(shape=capacity, dtype=np.int32),
+ 'reward': np.zeros(shape=capacity, dtype=np.float32),
+ 'next_obs': np.zeros(shape=(capacity, 4, 84, 84), dtype=np.uint8),
+ 'done': np.zeros(shape=capacity, dtype=np.bool)
+ }
+
+ # size of the buffer
+ self.size = 0
+
+ def add(self, obs, action, reward, next_obs, done):
+ """
+ ### Add sample to queue
+ """
+
+ idx = self.next_idx
+
+ # store in the queue
+ self.data['obs'][idx] = obs
+ self.data['action'][idx] = action
+ self.data['reward'][idx] = reward
+ self.data['next_obs'][idx] = next_obs
+ self.data['done'][idx] = done
+
+ # increment head of the queue and calculate the size
+ self.next_idx = (idx + 1) % self.capacity
+ self.size = min(self.capacity, self.size + 1)
+
+ # $p_i^\alpha$, new samples get `max_priority`
+ priority_alpha = self.max_priority ** self.alpha
+ self._set_priority_min(idx, priority_alpha)
+ self._set_priority_sum(idx, priority_alpha)
+
+ def _set_priority_min(self, idx, priority_alpha):
+ """
+ #### Set priority in binary segment tree for minimum
+ """
+
+ # leaf of the binary tree
+ idx += self.capacity
+ self.priority_min[idx] = priority_alpha
+
+ # update tree, by traversing along ancestors
+ while idx >= 2:
+ idx //= 2
+ self.priority_min[idx] = min(self.priority_min[2 * idx],
+ self.priority_min[2 * idx + 1])
+
+ def _set_priority_sum(self, idx, priority):
+ """
+ #### Set priority in binary segment tree for sum
+ """
+
+ # leaf of the binary tree
+ idx += self.capacity
+ self.priority_sum[idx] = priority
+
+ # update tree, by traversing along ancestors
+ while idx >= 2:
+ idx //= 2
+ self.priority_sum[idx] = self.priority_sum[2 * idx] + self.priority_sum[2 * idx + 1]
+
+ def _sum(self):
+ """
+ #### $\sum_k p_k^\alpha$
+ """
+ return self.priority_sum[1]
+
+ def _min(self):
+ """
+ #### $\min_k p_k^\alpha$
+ """
+ return self.priority_min[1]
+
+ def find_prefix_sum_idx(self, prefix_sum):
+ """
+ #### Find largest $i$ such that $\sum_{k=1}^{i} p_k^\alpha \le P$
+ """
+
+ # start from the root
+ idx = 1
+ while idx < self.capacity:
+ # if the sum of the left branch is higher than required sum
+ if self.priority_sum[idx * 2] > prefix_sum:
+ # go to left branch if the tree if the
+ idx = 2 * idx
+ else:
+ # otherwise go to right branch and reduce the sum of left
+ # branch from required sum
+ prefix_sum -= self.priority_sum[idx * 2]
+ idx = 2 * idx + 1
+
+ return idx - self.capacity
+
+ def sample(self, batch_size, beta):
+ """
+ ### Sample from buffer
+ """
+
+ samples = {
+ 'weights': np.zeros(shape=batch_size, dtype=np.float32),
+ 'indexes': np.zeros(shape=batch_size, dtype=np.int32)
+ }
+
+ # get samples
+ for i in range(batch_size):
+ p = random.random() * self._sum()
+ idx = self.find_prefix_sum_idx(p)
+ samples['indexes'][i] = idx
+
+ # $\min_i P(i) = \frac{\min_i p_i^\alpha}{\sum_k p_k^\alpha}$
+ prob_min = self._min() / self._sum()
+ # $\max_i w_i = \bigg(\frac{1}{N} \frac{1}{\min_i P(i)}\bigg)^\beta$
+ max_weight = (prob_min * self.size) ** (-beta)
+
+ for i in range(batch_size):
+ idx = samples['indexes'][i]
+ # $P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$
+ prob = self.priority_sum[idx + self.capacity] / self._sum()
+ # $w_i = \bigg(\frac{1}{N} \frac{1}{P(i)}\bigg)^\beta$
+ weight = (prob * self.size) ** (-beta)
+ # normalize by $\frac{1}{\max_i w_i}$,
+ # which also cancels off the $\frac{1}/{N}$ term
+ samples['weights'][i] = weight / max_weight
+
+ # get samples data
+ for k, v in self.data.items():
+ samples[k] = v[samples['indexes']]
+
+ return samples
+
+ def update_priorities(self, indexes, priorities):
+ """
+ ### Update priorities
+ """
+ for idx, priority in zip(indexes, priorities):
+ self.max_priority = max(self.max_priority, priority)
+
+ # $p_i^\alpha$
+ priority_alpha = priority ** self.alpha
+ self._set_priority_min(idx, priority_alpha)
+ self._set_priority_sum(idx, priority_alpha)
+
+ def is_full(self):
+ """
+ ### Is the buffer full
+
+ We only start sampling afte the buffer is full.
+ """
+ return self.capacity == self.size
diff --git a/labml_nn/rl/ppo/experiment.py b/labml_nn/rl/ppo/experiment.py
index 3f034959..e8d40b55 100644
--- a/labml_nn/rl/ppo/experiment.py
+++ b/labml_nn/rl/ppo/experiment.py
@@ -128,7 +128,7 @@ class Trainer:
# Value Loss
self.value_loss = ClippedValueFunctionLoss()
- def sample(self) -> (Dict[str, np.ndarray], List):
+ def sample(self) -> Dict[str, torch.Tensor]:
"""
### Sample data with current policy
"""