Overview of Actor-Critic
Actor-Critic is an approach to reinforcement learning that combines policies (policies) and value functions (value estimators). Actor-Critic combines the advantages of policy-based and value-based methods and aims to achieve efficient learning and control. The following is an overview of Actor-Critic.
1 Actor (policy network):
Actor is a neural network that represents a policy. The network learns a probability distribution that directly generates an action from a given state; Actor approximates the strategy and plays the role of action selection; in general, for continuous action spaces, Actor uses a probability density function (which outputs the mean and variance of the probability density function).
2. Critic (Value Network):
Critic is a value function for estimating state value or advantage. The value function evaluates the predicted reward or value for a given state or combination of states and actions, and the Critic assists in learning the strategy and points in the direction of improving the strategy.
3. Policy Update:
Actors and Critics learn cooperatively; Actors update measures and use information from Critics to select better actions. Typically, the policy is updated using the Policy Gradient method, which computes the gradient of the policy and optimizes it.
4. Value Estimation:
Critic calculates the predicted value of the reward and uses it to evaluate the measure. Typically, Temporal Difference (TD) errors are used to update the value function and assist in updating the policy.
5. Advantage Estimation:
Advantage is a measure of superiority in a given combination of states and actions. It indicates whether the combination is better than the average in the choice of actions, and advantage helps to improve the policy.
6. trade-off between utilization and exploration:
The Actor-Critic algorithm uses probabilistic measures to explore new actions while utilizing known information through the value function to improve measures. This tradeoff achieves a balance between stability and exploration capability.
Actor-Critic is effective for high-dimensional state spaces and continuous action spaces, making it a fluid method that can improve learning efficiency. Many variations and improvements have been proposed for this method and applied to a variety of tasks.
Algorithm used for Actor-Critic
Actor-Critic is a conceptual approach, and there are many variations of specific algorithms. The following describes several major algorithms for implementing the Actor-Critic architecture.
1. A2C (Advantage Actor-Critic):
A2C is a variant of the Actor-Critic architecture, a synchronous training algorithm in which the Actor (policy) and Critic (value function) are trained simultaneously and an advantage function is used to update the policy. Typically, the temporal difference (TD) error is computed to update the Critic and point out the direction of the policy. For details, please refer to “Overview of Advantage Actor-Critic (A2C), Algorithm and Example Implementation“.
2. A3C (Asynchronous Advantage Actor-Critic):
A3C is an asynchronous version of A2C in which multiple agents (Actors) learn independently in parallel and share their experience. A3C is a very efficient algorithm and takes advantage of parallel computation to achieve fast learning. For details, see “A3C (Asynchronous Advantage Actor-Critic) Overview, Algorithm, and Example Implementation.
3. DDPG (Deep Deterministic Policy Gradient):
DDPG is an algorithm that extends the Actor-Critic architecture to the continuous action space, where the Actor generates continuous actions and the Critic estimates the value of continuous actions. For more details, see “Deep Deterministic Policy Gradient (DDPG): Overview, Algorithm, and Example Implementation“.
4. TD3 (Twin Delayed Deep Deterministic Policy Gradient):
TD3 is an improved version of DDPG that uses two Critic networks to improve the stability of the value function estimation. It also introduces stochastic noise to enhance search and achieve stable learning. For details, please refer to “TD3 (Twin Delayed Deep Deterministic Policy Gradient): Overview, Algorithm, and Example Implementation.
5. SAC (Soft Actor-Critic):
SAC is an Actor-Critic architecture for continuous action spaces that learns soft policies. SAC is one of the most effective algorithms in continuous action spaces. For more information, see “Soft Actor-Critic (SAC) Overview, Algorithms, and Examples of Implementations.
These algorithms are based on the Actor-Critic architecture and are tailored to the properties of the state and action spaces. The choice of which algorithm to select depends on the nature of the problem and the requirements.
Example implementation of Actor-Critic
A simple example for implementing the Actor-Critic architecture is shown below. This example uses the OpenAI Gym’s CartPole environment, which provides Python code based on TensorFlow. This code is an implementation of the Advantage Actor-Critic (A2C) algorithm.
import numpy as np
import tensorflow as tf
import gym
# Setup of cartopole environment
env = gym.make('CartPole-v1')
state_dim = env.observation_space.shape[0]
n_actions = env.action_space.n
# Definition of Actor Network
actor = tf.keras.Sequential([
tf.keras.layers.Dense(64, activation='relu', input_shape=(state_dim,)),
tf.keras.layers.Dense(64, activation='relu'),
tf.keras.layers.Dense(n_actions, activation='softmax')
])
# Definition of Critic Network
critic = tf.keras.Sequential([
tf.keras.layers.Dense(64, activation='relu', input_shape=(state_dim,)),
tf.keras.layers.Dense(64, activation='relu'),
tf.keras.layers.Dense(1)
])
# Optimizer Definition
actor_optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
critic_optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
# hyperparameter
gamma = 0.99 # discount rate
num_episodes = 1000
for episode in range(num_episodes):
state = env.reset()
episode_states, episode_actions, episode_rewards = [], [], []
while True:
# Choose actions according to the Actor's strategy
action_probs = actor.predict(state.reshape(1, -1))
action = np.random.choice(n_actions, p=action_probs.ravel)
# Action implementation in the environment
next_state, reward, done, _ = env.step(action)
# Episode Recording
episode_states.append(state)
episode_actions.append(action)
episode_rewards.append(reward)
if done:
break
state = next_state
# Advantage Calculation
returns = []
G = 0
for t in range(len(episode_rewards) - 1, -1, -1):
G = episode_rewards[t] + gamma * G
returns.insert(0, G)
# Actor and Critic updates
with tf.GradientTape() as actor_tape, tf.GradientTape() as critic_tape:
action_masks = tf.one_hot(episode_actions, n_actions)
log_action_probs = tf.math.log(tf.reduce_sum(action_probs * action_masks, axis=1))
actor_loss = -tf.reduce_sum(log_action_probs * tf.convert_to_tensor(returns, dtype=tf.float32))
critic_loss = tf.reduce_mean((critic(tf.convert_to_tensor(episode_states, dtype=tf.float32)) - tf.convert_to_tensor(returns, dtype=tf.float32))**2)
actor_grads = actor_tape.gradient(actor_loss, actor.trainable_variables)
critic_grads = critic_tape.gradient(critic_loss, critic.trainable_variables)
actor_optimizer.apply_gradients(zip(actor_grads, actor.trainable_variables))
critic_optimizer.apply_gradients(zip(critic_grads, critic.trainable_variables))
if (episode + 1) % 10 == 0:
print(f"Episode {episode + 1}: Total Reward - {sum(episode_rewards)}")
env.close()This code is an example of an implementation of the Actor-Critic algorithm in a CartPole environment, where the actor and critic networks are trained in parallel and the measures and value functions are updated.
Challenge for Actor-Critic
There are several challenges and limitations to the Actor-Critic algorithm. The major challenges are described below.
1. high variance:
The Actor-Critic algorithm, which is based on the gradient method of learning measures, can have a high variance in learning measures. This is due to the episode-based learning method, which causes instability and slow convergence in learning.
2. hyperparameter selection:
The Actor-Critic algorithm needs to adjust many hyperparameters. For example, the choice of hyperparameters such as learning rate, discount rate, baseline function, entropy coefficient, etc. depends on the problem and is a difficult task to adjust.
3. impact of initialization:
The Actor-Critic algorithm may depend on initialization, and the method of initialization has a significant impact on the results. Incorrect initialization can negatively affect learning convergence.
4. appropriate reward design:
The Actor-Critic algorithm relies on a reward signal. Proper design of the reward is difficult, and an incorrect reward function can make learning difficult.
5. convergence to a locally optimal solution:
The Actor-Critic algorithm tends to converge to a local optimal solution and may have difficulty converging to a globally optimal solution.
6. handling non-stationary environments:
Actor-Critic may have difficulty responding appropriately to non-stationary environments and may limit the adaptability of the learned model when the environment changes.
Variance reduction methods, hyperparameter tuning, reward function design, improved initialization strategies, and the adoption of different Actor-Critic variants have been used to address these challenges. TRPO, described in “Overview of Trust Region Policy Optimization (TRPO), Algorithms, and Examples of Implementations“; Proximal Policy Optimization (PPO), described in “Overview of Proximal Policy Optimization (PPO), Algorithms, and Examples of Implementations“; and PPO, and SAC described in “Overview of Soft Actor-Critic (SAC), Algorithms, and Examples of Implementations” have been proposed to address the Actor-Critic challenge.
Addressing of the Challenge for Actor-Critic
The following methods and derived algorithms have been proposed to address the challenges of the Actor-Critic algorithm
1. variance reduction:
To reduce variance, a baseline function may be introduced. Baseline functions approximate the expected value of the reward and reduce the variance of the policy gradient, and state value functions (V-functions) and advantage functions are commonly used as baseline functions.
2. highly efficient learning:
In order to achieve efficient learning, the PPO described in “Overview of Proximal Policy Optimization (PPO), an improved version of the policy gradient method, and examples of algorithms and implementations” and TRPO described in “Overview of Trust Region Policy Optimization (TRPO), Algorithms, and Examples of Implementations“. These algorithms improve sample efficiency and learning stability.
3. Asynchronous Learning:
The Actor-Critic algorithm can be extended to asynchronous learning to take advantage of parallel computation and improve learning speed A3C described in “Overview of A3C (Asynchronous Advantage Actor-Critic) and Examples of Algorithms and Implementations,” and others incorporate this approach.
4. dealing with continuous action spaces:
To deal with continuous action spaces, DDPG described in “Overview, Algorithms, and Examples of Deep Deterministic Policy Gradient (DDPG)” and Soft Actor-Critic (SAC) described in “Overview, Algorithms, and Examples of Implementation of Soft Actor-Critic (SAC)” are examples of approaches for continuous action spaces.
5. entropy coefficient tuning:
Entropy coefficients can be introduced into the Actor-Critic algorithm to adjust the trade-off between search and control. The entropy coefficient enhances search by maximizing the entropy of the measures.
6. use of deep learning techniques:
The use of deep learning techniques is important to improve the performance of the Actor-Critic algorithm. The use of powerful neural network architectures and reinforcement learning libraries can help address the challenge.
References and Reference Books
Details of reinforcement learning are described in “Theories and Algorithms of Various Reinforcement Learning Techniques and Their Python Implementations. Please also refer to this page.
A reference book is “Reinforcement Learning: An Introduction, Second Edition.
“Deep Reinforcement Learning with Python: With PyTorch, TensorFlow and OpenAI Gym“
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