Configurations for Colab¶
import sys
IN_COLAB = "google.colab" in sys.modules
if IN_COLAB:
!apt install python-opengl
!apt install ffmpeg
!apt install xvfb
!pip install PyVirtualDisplay==3.0
!pip install gymnasium==0.28.1
from pyvirtualdisplay import Display
# Start virtual display
dis = Display(visible=0, size=(400, 400))
dis.start()
03. Prioritized Experience Replay (PER)¶
T. Schaul et al., "Prioritized Experience Replay." arXiv preprint arXiv:1511.05952, 2015.
Using a replay memory leads to design choices at two levels: which experiences to store, and which experiences to replay (and how to do so). This paper addresses only the latter: making the most effective use of the replay memory for learning, assuming that its contents are outside of our control.
The central component of prioritized replay is the criterion by which the importance of each transition is measured. A reasonable approach is to use the magnitude of a transition’s TD error δ, which indicates how ‘surprising’ or unexpected the transition is. This algorithm stores the last encountered TD error along with each transition in the replay memory. The transition with the largest absolute TD error is replayed from the memory. A Q-learning update is applied to this transition, which updates the weights in proportion to the TD error. One thing to note that new transitions arrive without a known TD-error, so it puts them at maximal priority in order to guarantee that all experience is seen at least once. (see store method)
We might use 2 ideas to deal with TD-error: 1. greedy TD-error prioritization, 2. stochastic prioritization. However, greedy TD-error prioritization has a severe drawback. Greedy prioritization focuses on a small subset of the experience: errors shrink slowly, especially when using function approximation, meaning that the initially high error transitions get replayed frequently. This lack of diversity that makes the system prone to over-fitting. To overcome this issue, we will use a stochastic sampling method that interpolates between pure greedy prioritization and uniform random sampling.
P(i)=pαi∑kpαkwhere pi>0 is the priority of transition i. The exponent α determines how much prioritization is used, with α=0 corresponding to the uniform case. In practice, we use additional term ϵ in order to guarantee all transactions can be possibly sampled: pi=|δi|+ϵ, where ϵ is a small positive constant.
One more. Let's recall one of the main ideas of DQN. To remove correlation of observations, it uses uniformly random sampling from the replay buffer. Prioritized replay introduces bias because it doesn't sample experiences uniformly at random due to the sampling proportion correspoding to TD-error. We can correct this bias by using importance-sampling (IS) weights
wi=(1N⋅1P(i))βthat fully compensates for the non-uniform probabilities P(i) if β=1. These weights can be folded into the Q-learning update by using wiδi instead of δi. In typical reinforcement learning scenarios, the unbiased nature of the updates is most important near convergence at the end of training, We therefore exploit the flexibility of annealing the amount of importance-sampling correction over time, by defining a schedule on the exponent β that reaches 1 only at the end of learning.
import os
import random
from typing import Dict, List, Tuple
import gymnasium as gym
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from IPython.display import clear_output
if IN_COLAB and not os.path.exists("segment_tree.py"):
# download segment tree module
!wget https://raw.githubusercontent.com/curt-park/rainbow-is-all-you-need/master/segment_tree.py
from segment_tree import MinSegmentTree, SumSegmentTree
/Users/jinwoo.park/miniforge3/envs/rainbow-is-all-you-need/lib/python3.8/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html from .autonotebook import tqdm as notebook_tqdm
Replay buffer¶
Please see 01.dqn.ipynb for detailed description.
class ReplayBuffer:
"""A simple numpy replay buffer."""
def __init__(self, obs_dim: int, size: int, batch_size: int = 32):
self.obs_buf = np.zeros([size, obs_dim], dtype=np.float32)
self.next_obs_buf = np.zeros([size, obs_dim], dtype=np.float32)
self.acts_buf = np.zeros([size], dtype=np.float32)
self.rews_buf = np.zeros([size], dtype=np.float32)
self.done_buf = np.zeros(size, dtype=np.float32)
self.max_size, self.batch_size = size, batch_size
self.ptr, self.size, = 0, 0
def store(
self,
obs: np.ndarray,
act: np.ndarray,
rew: float,
next_obs: np.ndarray,
done: bool,
):
self.obs_buf[self.ptr] = obs
self.next_obs_buf[self.ptr] = next_obs
self.acts_buf[self.ptr] = act
self.rews_buf[self.ptr] = rew
self.done_buf[self.ptr] = done
self.ptr = (self.ptr + 1) % self.max_size
self.size = min(self.size + 1, self.max_size)
def sample_batch(self) -> Dict[str, np.ndarray]:
idxs = np.random.choice(self.size, size=self.batch_size, replace=False)
return dict(obs=self.obs_buf[idxs],
next_obs=self.next_obs_buf[idxs],
acts=self.acts_buf[idxs],
rews=self.rews_buf[idxs],
done=self.done_buf[idxs])
def __len__(self) -> int:
return self.size
Prioritized replay Buffer¶
The key concept of PER's implementation is Segment Tree. It efficiently stores and samples transitions while managing the priorities of them. We recommend you understand how it works before you move on. Here are references for you:
class PrioritizedReplayBuffer(ReplayBuffer):
"""Prioritized Replay buffer.
Attributes:
max_priority (float): max priority
tree_ptr (int): next index of tree
alpha (float): alpha parameter for prioritized replay buffer
sum_tree (SumSegmentTree): sum tree for prior
min_tree (MinSegmentTree): min tree for min prior to get max weight
"""
def __init__(
self,
obs_dim: int,
size: int,
batch_size: int = 32,
alpha: float = 0.6
):
"""Initialization."""
assert alpha >= 0
super(PrioritizedReplayBuffer, self).__init__(obs_dim, size, batch_size)
self.max_priority, self.tree_ptr = 1.0, 0
self.alpha = alpha
# capacity must be positive and a power of 2.
tree_capacity = 1
while tree_capacity < self.max_size:
tree_capacity *= 2
self.sum_tree = SumSegmentTree(tree_capacity)
self.min_tree = MinSegmentTree(tree_capacity)
def store(
self,
obs: np.ndarray,
act: int,
rew: float,
next_obs: np.ndarray,
done: bool
):
"""Store experience and priority."""
super().store(obs, act, rew, next_obs, done)
self.sum_tree[self.tree_ptr] = self.max_priority ** self.alpha
self.min_tree[self.tree_ptr] = self.max_priority ** self.alpha
self.tree_ptr = (self.tree_ptr + 1) % self.max_size
def sample_batch(self, beta: float = 0.4) -> Dict[str, np.ndarray]:
"""Sample a batch of experiences."""
assert len(self) >= self.batch_size
assert beta > 0
indices = self._sample_proportional()
obs = self.obs_buf[indices]
next_obs = self.next_obs_buf[indices]
acts = self.acts_buf[indices]
rews = self.rews_buf[indices]
done = self.done_buf[indices]
weights = np.array([self._calculate_weight(i, beta) for i in indices])
return dict(
obs=obs,
next_obs=next_obs,
acts=acts,
rews=rews,
done=done,
weights=weights,
indices=indices,
)
def update_priorities(self, indices: List[int], priorities: np.ndarray):
"""Update priorities of sampled transitions."""
assert len(indices) == len(priorities)
for idx, priority in zip(indices, priorities):
assert priority > 0
assert 0 <= idx < len(self)
self.sum_tree[idx] = priority ** self.alpha
self.min_tree[idx] = priority ** self.alpha
self.max_priority = max(self.max_priority, priority)
def _sample_proportional(self) -> List[int]:
"""Sample indices based on proportions."""
indices = []
p_total = self.sum_tree.sum(0, len(self) - 1)
segment = p_total / self.batch_size
for i in range(self.batch_size):
a = segment * i
b = segment * (i + 1)
upperbound = random.uniform(a, b)
idx = self.sum_tree.retrieve(upperbound)
indices.append(idx)
return indices
def _calculate_weight(self, idx: int, beta: float):
"""Calculate the weight of the experience at idx."""
# get max weight
p_min = self.min_tree.min() / self.sum_tree.sum()
max_weight = (p_min * len(self)) ** (-beta)
# calculate weights
p_sample = self.sum_tree[idx] / self.sum_tree.sum()
weight = (p_sample * len(self)) ** (-beta)
weight = weight / max_weight
return weight
Network¶
We are going to use a simple network architecture with three fully connected layers and two non-linearity functions (ReLU).
class Network(nn.Module):
def __init__(self, in_dim: int, out_dim: int):
"""Initialization."""
super(Network, self).__init__()
self.layers = nn.Sequential(
nn.Linear(in_dim, 128),
nn.ReLU(),
nn.Linear(128, 128),
nn.ReLU(),
nn.Linear(128, out_dim)
)
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""Forward method implementation."""
return self.layers(x)
DQN + PER Agent¶
Here is a summary of DQNAgent class.
| Method | Note |
|---|---|
| select_action | select an action from the input state. |
| step | take an action and return the response of the env. |
| compute_dqn_loss | return dqn loss. |
| update_model | update the model by gradient descent. |
| target_hard_update | hard update from the local model to the target model. |
| train | train the agent during num_frames. |
| test | test the agent (1 episode). |
| plot | plot the training progresses. |
All differences from pure DQN are noted with comments - PER.
init¶
Here, we use PrioritizedReplayBuffer, instead of ReplayBuffer, and use hold 2 more parameters beta and priority epsilon which are used to calculate weights and new priorities respectively.
compute_dqn_loss & update_model¶
It returns every loss per each sample for importance sampling before average. After updating the nework, it is necessary to update priorities of all sampled experiences.
train¶
beta linearly increases to 1 at every training step.
class DQNAgent:
"""DQN Agent interacting with environment.
Attribute:
env (gym.Env): openAI Gym environment
memory (ReplayBuffer): replay memory to store transitions
batch_size (int): batch size for sampling
epsilon (float): parameter for epsilon greedy policy
epsilon_decay (float): step size to decrease epsilon
max_epsilon (float): max value of epsilon
min_epsilon (float): min value of epsilon
target_update (int): period for target model's hard update
gamma (float): discount factor
dqn (Network): model to train and select actions
dqn_target (Network): target model to update
optimizer (torch.optim): optimizer for training dqn
transition (list): transition information including
state, action, reward, next_state, done
beta (float): determines how much importance sampling is used
prior_eps (float): guarantees every transition can be sampled
"""
def __init__(
self,
env: gym.Env,
memory_size: int,
batch_size: int,
target_update: int,
epsilon_decay: float,
seed: int,
max_epsilon: float = 1.0,
min_epsilon: float = 0.1,
gamma: float = 0.99,
# PER parameters
alpha: float = 0.2,
beta: float = 0.6,
prior_eps: float = 1e-6,
):
"""Initialization.
Args:
env (gym.Env): openAI Gym environment
memory_size (int): length of memory
batch_size (int): batch size for sampling
target_update (int): period for target model's hard update
epsilon_decay (float): step size to decrease epsilon
lr (float): learning rate
max_epsilon (float): max value of epsilon
min_epsilon (float): min value of epsilon
gamma (float): discount factor
alpha (float): determines how much prioritization is used
beta (float): determines how much importance sampling is used
prior_eps (float): guarantees every transition can be sampled
"""
obs_dim = env.observation_space.shape[0]
action_dim = env.action_space.n
self.env = env
self.batch_size = batch_size
self.epsilon = max_epsilon
self.epsilon_decay = epsilon_decay
self.seed = seed
self.max_epsilon = max_epsilon
self.min_epsilon = min_epsilon
self.target_update = target_update
self.gamma = gamma
# device: cpu / gpu
self.device = torch.device(
"cuda" if torch.cuda.is_available() else "cpu"
)
print(self.device)
# PER
# In DQN, We used "ReplayBuffer(obs_dim, memory_size, batch_size)"
self.beta = beta
self.prior_eps = prior_eps
self.memory = PrioritizedReplayBuffer(
obs_dim, memory_size, batch_size, alpha
)
# networks: dqn, dqn_target
self.dqn = Network(obs_dim, action_dim).to(self.device)
self.dqn_target = Network(obs_dim, action_dim).to(self.device)
self.dqn_target.load_state_dict(self.dqn.state_dict())
self.dqn_target.eval()
# optimizer
self.optimizer = optim.Adam(self.dqn.parameters())
# transition to store in memory
self.transition = list()
# mode: train / test
self.is_test = False
def select_action(self, state: np.ndarray) -> np.ndarray:
"""Select an action from the input state."""
# epsilon greedy policy
if self.epsilon > np.random.random():
selected_action = self.env.action_space.sample()
else:
selected_action = self.dqn(
torch.FloatTensor(state).to(self.device)
).argmax()
selected_action = selected_action.detach().cpu().numpy()
if not self.is_test:
self.transition = [state, selected_action]
return selected_action
def step(self, action: np.ndarray) -> Tuple[np.ndarray, np.float64, bool]:
"""Take an action and return the response of the env."""
next_state, reward, terminated, truncated, _ = self.env.step(action)
done = terminated or truncated
if not self.is_test:
self.transition += [reward, next_state, done]
self.memory.store(*self.transition)
return next_state, reward, done
def update_model(self) -> torch.Tensor:
"""Update the model by gradient descent."""
# PER needs beta to calculate weights
samples = self.memory.sample_batch(self.beta)
weights = torch.FloatTensor(
samples["weights"].reshape(-1, 1)
).to(self.device)
indices = samples["indices"]
# PER: importance sampling before average
elementwise_loss = self._compute_dqn_loss(samples)
loss = torch.mean(elementwise_loss * weights)
self.optimizer.zero_grad()
loss.backward()
self.optimizer.step()
# PER: update priorities
loss_for_prior = elementwise_loss.detach().cpu().numpy()
new_priorities = loss_for_prior + self.prior_eps
self.memory.update_priorities(indices, new_priorities)
return loss.item()
def train(self, num_frames: int, plotting_interval: int = 200):
"""Train the agent."""
self.is_test = False
state, _ = self.env.reset(seed=self.seed)
update_cnt = 0
epsilons = []
losses = []
scores = []
score = 0
for frame_idx in range(1, num_frames + 1):
action = self.select_action(state)
next_state, reward, done = self.step(action)
state = next_state
score += reward
# PER: increase beta
fraction = min(frame_idx / num_frames, 1.0)
self.beta = self.beta + fraction * (1.0 - self.beta)
# if episode ends
if done:
state, _ = self.env.reset(seed=self.seed)
scores.append(score)
score = 0
# if training is ready
if len(self.memory) >= self.batch_size:
loss = self.update_model()
losses.append(loss)
update_cnt += 1
# linearly decrease epsilon
self.epsilon = max(
self.min_epsilon, self.epsilon - (
self.max_epsilon - self.min_epsilon
) * self.epsilon_decay
)
epsilons.append(self.epsilon)
# if hard update is needed
if update_cnt % self.target_update == 0:
self._target_hard_update()
# plotting
if frame_idx % plotting_interval == 0:
self._plot(frame_idx, scores, losses, epsilons)
self.env.close()
def test(self, video_folder: str) -> None:
"""Test the agent."""
self.is_test = True
# for recording a video
naive_env = self.env
self.env = gym.wrappers.RecordVideo(self.env, video_folder=video_folder)
state, _ = self.env.reset(seed=self.seed)
done = False
score = 0
while not done:
action = self.select_action(state)
next_state, reward, done = self.step(action)
state = next_state
score += reward
print("score: ", score)
self.env.close()
# reset
self.env = naive_env
def _compute_dqn_loss(self, samples: Dict[str, np.ndarray]) -> torch.Tensor:
"""Return dqn loss."""
device = self.device # for shortening the following lines
state = torch.FloatTensor(samples["obs"]).to(device)
next_state = torch.FloatTensor(samples["next_obs"]).to(device)
action = torch.LongTensor(samples["acts"].reshape(-1, 1)).to(device)
reward = torch.FloatTensor(samples["rews"].reshape(-1, 1)).to(device)
done = torch.FloatTensor(samples["done"].reshape(-1, 1)).to(device)
# G_t = r + gamma * v(s_{t+1}) if state != Terminal
# = r otherwise
curr_q_value = self.dqn(state).gather(1, action)
next_q_value = self.dqn_target(
next_state
).max(dim=1, keepdim=True)[0].detach()
mask = 1 - done
target = (reward + self.gamma * next_q_value * mask).to(self.device)
# calculate element-wise dqn loss
elementwise_loss = F.smooth_l1_loss(curr_q_value, target, reduction="none")
return elementwise_loss
def _target_hard_update(self):
"""Hard update: target <- local."""
self.dqn_target.load_state_dict(self.dqn.state_dict())
def _plot(
self,
frame_idx: int,
scores: List[float],
losses: List[float],
epsilons: List[float],
):
"""Plot the training progresses."""
clear_output(True)
plt.figure(figsize=(20, 5))
plt.subplot(131)
plt.title('frame %s. score: %s' % (frame_idx, np.mean(scores[-10:])))
plt.plot(scores)
plt.subplot(132)
plt.title('loss')
plt.plot(losses)
plt.subplot(133)
plt.title('epsilons')
plt.plot(epsilons)
plt.show()
Environment¶
You can see the code and configurations of CartPole-v1 from Farama Gymnasium's repository.
# environment
env = gym.make("CartPole-v1", max_episode_steps=200, render_mode="rgb_array")
Set random seed¶
seed = 777
def seed_torch(seed):
torch.manual_seed(seed)
if torch.backends.cudnn.enabled:
torch.cuda.manual_seed(seed)
torch.backends.cudnn.benchmark = False
torch.backends.cudnn.deterministic = True
np.random.seed(seed)
random.seed(seed)
seed_torch(seed)
Initialize¶
# parameters
num_frames = 10000
memory_size = 1000
batch_size = 32
target_update = 150
epsilon_decay = 1 / 2000
# train
agent = DQNAgent(env, memory_size, batch_size, target_update, epsilon_decay, seed)
cpu
Train¶
agent.train(num_frames)
Test¶
Run the trained agent (1 episode).
video_folder="videos/per"
agent.test(video_folder=video_folder)
Moviepy - Building video /Users/jinwoo.park/Repositories/rainbow-is-all-you-need/videos/per/rl-video-episode-0.mp4. Moviepy - Writing video /Users/jinwoo.park/Repositories/rainbow-is-all-you-need/videos/per/rl-video-episode-0.mp4
Moviepy - Done ! Moviepy - video ready /Users/jinwoo.park/Repositories/rainbow-is-all-you-need/videos/per/rl-video-episode-0.mp4 score: 102.0
Render¶
import base64
import glob
import io
import os
from IPython.display import HTML, display
def ipython_show_video(path: str) -> None:
"""Show a video at `path` within IPython Notebook."""
if not os.path.isfile(path):
raise NameError("Cannot access: {}".format(path))
video = io.open(path, "r+b").read()
encoded = base64.b64encode(video)
display(HTML(
data="""
<video width="320" height="240" alt="test" controls>
<source src="data:video/mp4;base64,{0}" type="video/mp4"/>
</video>
""".format(encoded.decode("ascii"))
))
def show_latest_video(video_folder: str) -> str:
"""Show the most recently recorded video from video folder."""
list_of_files = glob.glob(os.path.join(video_folder, "*.mp4"))
latest_file = max(list_of_files, key=os.path.getctime)
ipython_show_video(latest_file)
return latest_file
latest_file = show_latest_video(video_folder=video_folder)
print("Played:", latest_file)
Played: videos/per/rl-video-episode-0.mp4