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
from pyvirtualdisplay import Display
# Start virtual display
dis = Display(visible=0, size=(600, 400))
dis.start()
In value-based reinforcement learning methods, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. However, similar issues with actor-critic methods in continuous control domains have been largely left untouched (See paper for detailed description). To solve this problem, this paper proposes a clipped Double Q-learning. In addtion, this paper contains a number of components that address variance reduction.
The author's modifications are applied to actor-critic method for continuous control, Deep Deterministic Policy Gradient algorithm (DDPG), to form the Twin Delayed Deep Deterministic policy gradient algorithm (TD3).
For learning in high-dimentional and continous action spaces, the authors of DDPG combine the actor-critic approach with insights from the success of DQN. Deep DPG(DDPG) is based on the deterministic policy gradient(DPG) algorithm (Silver et al., 2014). Please see 03.DDPG.ipynb for detailed description of DDPG.
In Double DQN (Van Hasselt et al., 2016), the authors propose using the target network as one of the value estimates, and obtain a policy by greedy maximization of the current value network rather than the target network. In an actor-critic setting, an analogous update uses the current policy rather than the target policy in the learning target. However, with the slow-changing policy in actor-critic, the current and target networks were too similar to make an independent estimation, and offered little improvement. Instead, the original Double Q-learning formulation can be used, with a pair of actors $(\pi_{\phi_1}, \pi_{\phi_2})$ and critics $(Q_{\theta_1}, Q_{\theta_2})$, where $\pi_{\phi_1}$ is optimized with respect to $Q_{\theta_1}$ and $\pi_{\phi_2}$ with respect to $Q_{\theta_2}$:
$$ y_1 = r + \gamma Q_{\theta'_2} (s' , \pi_{\phi_1}(s')) \\ y_2 = r + \gamma Q_{\theta'_1} (s' , \pi_{\phi_2}(s')) $$The critics are not entirely independent, due to the use of the opposite critic in the learning targets, as well as the same replay buffer. As a result, for some states we will have $Q_{\theta'_2}(s, \pi_{\phi_1}) > Q_{\theta'_1}(s, \pi_{\phi_1})$. This is problematic because $Q_{\theta'_1}(s, \pi_{\phi_1})$ will generally overestimate the true value, and in certain areas of the state space the overestimation will be further exaggerated. To address this problem, the authors propose to take the minimum between the two estimates:
$$ y_1 = r + \gamma \underset{i=1,2}{\min} Q_{\theta'_i} (s' , \pi_{\phi_1}(s')) $$If policy updates on high-error states cause different behavior, then the policy network should be updated at a lower frequency than the value network, to first minimize error before introducing a policy update. The authors propose delaying policy updates until the value error is as small as possible.
When updating the critic, a learning target using a deterministic policy is highly susceptible to in accuracies induced by function approximation error, increasing the variance of the target. This induced variance can be reduced through regularization. The authors propose that fitting the value of a small area around the target action
$$ y = r + E_\epsilon [Q_{\theta'}(s', \pi_{\phi '}(s') + \epsilon], $$would have the benefit of smoothing the value estimate by bootstrapping off of similar state-action value estimates. In practice, this makes below:
$$ y = r + \gamma Q_{\theta '}(s', \pi_{\phi '}(s') + \epsilon), \\ \epsilon \sim \text{clip} (\mathcal(N)(0, \sigma), -c, c), $$where the added noise is clipped to keep the target close tothe original action.
import copy
import os
import random
from typing import Dict, List, Tuple
import 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 torch.backends.cudnn.enabled:
torch.backends.cudnn.benchmark = False
torch.backends.cudnn.deterministic = True
seed = 777
torch.manual_seed(seed)
np.random.seed(seed)
random.seed(seed)
Typically, people implement replay buffers with one of the following three data structures:
deque is very easy to handle once you initialize its maximum length (e.g. deque(maxlen=buffer_size)). However, the indexing operation of deque gets terribly slow as it grows up because it is internally doubly linked list. On the other hands, list is an array, so it is relatively faster than deque when you sample batches at every step. Its amortized cost of Get item is O(1).
Last but not least, let's see numpy.ndarray. numpy.ndarray is even faster than list due to the fact that it is a homogeneous array of fixed-size items, so you can get the benefits of locality of reference, . Whereas list is an array of pointers to objects, even when all of them are of the same type.
Here, we are going to implement a replay buffer using numpy.ndarray.
Reference:
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
Because the DDPG and the TD3 policy is deterministic, it's not enough to explore a wide variety of actions. In order to facilitate more exploration. TD3 adds Gaussian noise to each action, while DDPG uses Ornstein-Uhlenbeck noise. The TD3 paper states Ornstein-Uhlenbeck noise offered no performance benefits.
class GaussianNoise:
"""Gaussian Noise.
Taken from https://github.com/vitchyr/rlkit
"""
def __init__(
self,
action_dim: int,
min_sigma: float = 1.0,
max_sigma: float = 1.0,
decay_period: int = 1000000,
):
"""Initialize."""
self.action_dim = action_dim
self.max_sigma = max_sigma
self.min_sigma = min_sigma
self.decay_period = decay_period
def sample(self, t: int = 0) -> float:
"""Get an action with gaussian noise."""
sigma = self.max_sigma - (self.max_sigma - self.min_sigma) * min(
1.0, t / self.decay_period
)
return np.random.normal(0, sigma, size=self.action_dim)
We are going to use two separated networks for actor and critic. The actor network has three fully connected layers and three non-linearity functions, ReLU for hidden layers and tanh for the output layer. On the other hand, the critic network has three fully connected layers, but it used two activation functions for hidden layers ReLU. Plus, its input sizes of critic network are sum of state sizes and action sizes. One thing to note is that we initialize the final layer's weights and biases so that they are uniformly distributed.
class Actor(nn.Module):
def __init__(self, in_dim: int, out_dim: int, init_w: float = 3e-3):
"""Initialize."""
super(Actor, self).__init__()
self.hidden1 = nn.Linear(in_dim, 128)
self.hidden2 = nn.Linear(128, 128)
self.out = nn.Linear(128, out_dim)
self.out.weight.data.uniform_(-init_w, init_w)
self.out.bias.data.uniform_(-init_w, init_w)
def forward(self, state: torch.Tensor) -> torch.Tensor:
"""Forward method implementation."""
x = F.relu(self.hidden1(state))
x = F.relu(self.hidden2(x))
action = self.out(x).tanh()
return action
class Critic(nn.Module):
def __init__(self, in_dim: int, init_w: float = 3e-3):
"""Initialize."""
super(Critic, self).__init__()
self.hidden1 = nn.Linear(in_dim, 128)
self.hidden2 = nn.Linear(128, 128)
self.out = nn.Linear(128, 1)
self.out.weight.data.uniform_(-init_w, init_w)
self.out.bias.data.uniform_(-init_w, init_w)
def forward(self, state: torch.Tensor, action: torch.Tensor) -> torch.Tensor:
"""Forward method implementation."""
x = torch.cat((state, action), dim=-1)
x = F.relu(self.hidden1(x))
x = F.relu(self.hidden2(x))
value = self.out(x)
return value
Here is a summary of TD3Agent class.
Method | Note |
---|---|
select_action | select an action from the input state. |
step | take an action and return the response of the env. |
update_model | update the model by gradient descent. |
train | train the agent during num_frames. |
test | test the agent (1 episode). |
_target_soft_update | soft update from the local model to the target model. |
_plot | plot the training progresses. |
class TD3Agent:
"""TD3Agent interacting with environment.
Attribute:
env (gym.Env): openAI Gym environment
actor1 (nn.Module): target actor model to select actions
actor2 (nn.Module): target actor model to select actions
actor_target1 (nn.Module): actor model to predict next actions
actor_target2 (nn.Module): actor model to predict next actions
actor_optimizer (Optimizer): optimizer for training actor
critic1 (nn.Module): critic model to predict state values
critic2 (nn.Module): critic model to predict state values
critic_target1 (nn.Module): target critic model to predict state values
critic_target2 (nn.Module): target critic model to predict state values
critic_optimizer (Optimizer): optimizer for training critic
memory (ReplayBuffer): replay memory to store transitions
batch_size (int): batch size for sampling
gamma (float): discount factor
tau (float): parameter for soft target update
initial_random_steps (int): initial random action steps
exploration_noise (GaussianNoise): gaussian noise for policy
target_policy_noise (GaussianNoise): gaussian noise for target policy
target_policy_noise_clip (float): clip target gaussian noise
device (torch.device): cpu / gpu
transition (list): temporory storage for the recent transition
policy_update_freq (int): update actor every time critic updates this times
total_step (int): total step numbers
is_test (bool): flag to show the current mode (train / test)
"""
def __init__(
self,
env: gym.Env,
memory_size: int,
batch_size: int,
gamma: float = 0.99,
tau: float = 5e-3,
exploration_noise: float = 0.1,
target_policy_noise: float = 0.2,
target_policy_noise_clip: float = 0.5,
initial_random_steps: int = int(1e4),
policy_update_freq: int = 2,
):
"""Initialize."""
obs_dim = env.observation_space.shape[0]
action_dim = env.action_space.shape[0]
self.env = env
self.memory = ReplayBuffer(obs_dim, memory_size, batch_size)
self.batch_size = batch_size
self.gamma = gamma
self.tau = tau
self.initial_random_steps = initial_random_steps
self.policy_update_freq = policy_update_freq
# device: cpu / gpu
self.device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
print(self.device)
# noise
self.exploration_noise = GaussianNoise(
action_dim, exploration_noise, exploration_noise
)
self.target_policy_noise = GaussianNoise(
action_dim, target_policy_noise, target_policy_noise
)
self.target_policy_noise_clip = target_policy_noise_clip
# networks
self.actor = Actor(obs_dim, action_dim).to(self.device)
self.actor_target = Actor(obs_dim, action_dim).to(self.device)
self.actor_target.load_state_dict(self.actor.state_dict())
self.critic1 = Critic(obs_dim + action_dim).to(self.device)
self.critic_target1 = Critic(obs_dim + action_dim).to(self.device)
self.critic_target1.load_state_dict(self.critic1.state_dict())
self.critic2 = Critic(obs_dim + action_dim).to(self.device)
self.critic_target2 = Critic(obs_dim + action_dim).to(self.device)
self.critic_target2.load_state_dict(self.critic2.state_dict())
# concat critic parameters to use one optim
critic_parameters = list(self.critic1.parameters()) + list(
self.critic2.parameters()
)
# optimizer
self.actor_optimizer = optim.Adam(self.actor.parameters(), lr=3e-4)
self.critic_optimizer = optim.Adam(critic_parameters, lr=1e-3)
# transition to store in memory
self.transition = list()
# total steps count
self.total_step = 0
# update step for actor
self.update_step = 0
# mode: train / test
self.is_test = False
def select_action(self, state: np.ndarray) -> np.ndarray:
"""Select an action from the input state."""
# if initial random action should be conducted
if self.total_step < self.initial_random_steps and not self.is_test:
selected_action = self.env.action_space.sample()
else:
selected_action = (
self.actor(torch.FloatTensor(state).to(self.device))[0]
.detach()
.cpu()
.numpy()
)
# add noise for exploration during training
if not self.is_test:
noise = self.exploration_noise.sample()
selected_action = np.clip(
selected_action + noise, -1.0, 1.0
)
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, done, _ = self.env.step(action)
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."""
device = self.device # for shortening the following lines
samples = self.memory.sample_batch()
states = torch.FloatTensor(samples["obs"]).to(device)
next_states = torch.FloatTensor(samples["next_obs"]).to(device)
actions = torch.FloatTensor(samples["acts"].reshape(-1, 1)).to(device)
rewards = torch.FloatTensor(samples["rews"].reshape(-1, 1)).to(device)
dones = torch.FloatTensor(samples["done"].reshape(-1, 1)).to(device)
masks = 1 - dones
# get actions with noise
noise = torch.FloatTensor(self.target_policy_noise.sample()).to(device)
clipped_noise = torch.clamp(
noise, -self.target_policy_noise_clip, self.target_policy_noise_clip
)
next_actions = (self.actor_target(next_states) + clipped_noise).clamp(
-1.0, 1.0
)
# min (Q_1', Q_2')
next_values1 = self.critic_target1(next_states, next_actions)
next_values2 = self.critic_target2(next_states, next_actions)
next_values = torch.min(next_values1, next_values2)
# G_t = r + gamma * v(s_{t+1}) if state != Terminal
# = r otherwise
curr_returns = rewards + self.gamma * next_values * masks
curr_returns = curr_returns.detach()
# critic loss
values1 = self.critic1(states, actions)
values2 = self.critic2(states, actions)
critic1_loss = F.mse_loss(values1, curr_returns)
critic2_loss = F.mse_loss(values2, curr_returns)
# train critic
critic_loss = critic1_loss + critic2_loss
self.critic_optimizer.zero_grad()
critic_loss.backward()
self.critic_optimizer.step()
if self.total_step % self.policy_update_freq == 0:
# train actor
actor_loss = -self.critic1(states, self.actor(states)).mean()
self.actor_optimizer.zero_grad()
actor_loss.backward()
self.actor_optimizer.step()
# target update
self._target_soft_update()
else:
actor_loss = torch.zeros(1)
return actor_loss.data, critic_loss.data
def train(self, num_frames: int, plotting_interval: int = 200):
"""Train the agent."""
self.is_test = False
state = self.env.reset()
actor_losses = []
critic_losses = []
scores = []
score = 0
for self.total_step in range(1, num_frames + 1):
action = self.select_action(state)
next_state, reward, done = self.step(action)
state = next_state
score += reward
# if episode ends
if done:
state = env.reset()
scores.append(score)
score = 0
# if training is ready
if (
len(self.memory) >= self.batch_size
and self.total_step > self.initial_random_steps
):
actor_loss, critic_loss = self.update_model()
actor_losses.append(actor_loss)
critic_losses.append(critic_loss)
# plotting
if self.total_step % plotting_interval == 0:
self._plot(self.total_step, scores, actor_losses, critic_losses)
self.env.close()
def test(self):
"""Test the agent."""
self.is_test = True
state = self.env.reset()
done = False
score = 0
frames = []
while not done:
frames.append(self.env.render(mode="rgb_array"))
action = self.select_action(state)
next_state, reward, done = self.step(action)
state = next_state
score += reward
print("score: ", score)
self.env.close()
return frames
def _target_soft_update(self):
"""Soft-update: target = tau*local + (1-tau)*target."""
tau = self.tau
for t_param, l_param in zip(
self.actor_target.parameters(), self.actor.parameters()
):
t_param.data.copy_(tau * l_param.data + (1.0 - tau) * t_param.data)
for t_param, l_param in zip(
self.critic_target1.parameters(), self.critic1.parameters()
):
t_param.data.copy_(tau * l_param.data + (1.0 - tau) * t_param.data)
for t_param, l_param in zip(
self.critic_target2.parameters(), self.critic2.parameters()
):
t_param.data.copy_(tau * l_param.data + (1.0 - tau) * t_param.data)
def _plot(
self,
frame_idx: int,
scores: List[float],
actor_losses: List[float],
critic_losses: List[float],
):
"""Plot the training progresses."""
clear_output(True)
plt.figure(figsize=(30, 5))
plt.subplot(131)
plt.title("frame %s. score: %s" % (frame_idx, np.mean(scores[-10:])))
plt.plot(scores)
plt.subplot(132)
plt.title("actor_loss")
plt.plot(actor_losses)
plt.subplot(133)
plt.title("critic_loss")
plt.plot(critic_losses)
plt.show()
ActionNormalizer is an action wrapper class to normalize the action values ranged in (-1. 1). Thanks to this class, we can make the agent simply select action values within the zero centered range (-1, 1).
class ActionNormalizer(gym.ActionWrapper):
"""Rescale and relocate the actions."""
def action(self, action: np.ndarray) -> np.ndarray:
"""Change the range (-1, 1) to (low, high)."""
low = self.action_space.low
high = self.action_space.high
scale_factor = (high - low) / 2
reloc_factor = high - scale_factor
action = action * scale_factor + reloc_factor
action = np.clip(action, low, high)
return action
def reverse_action(self, action: np.ndarray) -> np.ndarray:
"""Change the range (low, high) to (-1, 1)."""
low = self.action_space.low
high = self.action_space.high
scale_factor = (high - low) / 2
reloc_factor = high - scale_factor
action = (action - reloc_factor) / scale_factor
action = np.clip(action, -1.0, 1.0)
return action
You can see the code and configurations of Pendulum-v0 from OpenAI's repository.
# environment
env_id = "Pendulum-v0"
env = gym.make(env_id)
env = ActionNormalizer(env)
env.seed(seed)
/home/khkim/anaconda3/envs/pg-is-all-you-need/lib/python3.6/site-packages/gym/logger.py:30: UserWarning: WARN: Box bound precision lowered by casting to float32
warnings.warn(colorize('%s: %s'%('WARN', msg % args), 'yellow'))
[777]
# parameters
num_frames = 50000
memory_size = 100000
batch_size = 128
initial_random_steps = 10000
agent = TD3Agent(
env, memory_size, batch_size, initial_random_steps=initial_random_steps
)
cpu
agent.train(num_frames)
Run the trained agent (1 episode).
# test
if IN_COLAB:
agent.env = gym.wrappers.Monitor(agent.env, "videos", force=True)
frames = agent.test()
score: -235.42615105825175
if IN_COLAB: # for colab
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 alt="test" controls>
<source src="data:video/mp4;base64,{0}" type="video/mp4"/>
</video>
""".format(encoded.decode("ascii"))
))
list_of_files = glob.glob("videos/*.mp4")
latest_file = max(list_of_files, key=os.path.getctime)
print(latest_file)
ipython_show_video(latest_file)
else: # for jupyter
from matplotlib import animation
from JSAnimation.IPython_display import display_animation
from IPython.display import display
def display_frames_as_gif(frames):
"""Displays a list of frames as a gif, with controls."""
patch = plt.imshow(frames[0])
plt.axis('off')
def animate(i):
patch.set_data(frames[i])
anim = animation.FuncAnimation(
plt.gcf(), animate, frames = len(frames), interval=50
)
display(display_animation(anim, default_mode='loop'))
# display
display_frames_as_gif(frames)