Policy Gradients - Tutorial

Policy gradients are a class of algorithms used in reinforcement learning, a subset of artificial neural networks (ANN). Unlike value-based methods that aim to estimate the action-values, policy gradients directly learn a policy that maps states to actions. Policy gradients are particularly well-suited for tasks with continuous action spaces, as they can directly optimize the policy without the need for a value function. In this tutorial, we will explore the concepts of policy gradients and how to implement them.

Introduction to Policy Gradients

In reinforcement learning, the goal of an agent is to learn a policy, denoted as π(a|s), that specifies the probability of taking action 'a' given state 's'. The objective of policy gradient algorithms is to maximize the expected cumulative reward, also known as the return, by updating the parameters of the policy. Policy gradients are especially effective in scenarios where the action space is continuous and the optimal policy is not easily parameterized by a value function.

Steps in Implementing Policy Gradients

Implementing policy gradients involves the following key steps:

Step 1: Define the Policy

Choose a parametric form for the policy π(a|s). Common choices include Gaussian policies for continuous action spaces and softmax policies for discrete action spaces.

Step 2: Collect Trajectories

Collect trajectories by interacting with the environment using the current policy. A trajectory consists of a sequence of states, actions, and rewards encountered during an episode. These trajectories are used to estimate the gradient of the expected cumulative reward.

Step 3: Compute the Objective Function

Compute the objective function, typically referred to as the policy gradient, which estimates the gradient of the expected cumulative reward with respect to the policy parameters. The policy gradient is derived using the likelihood ratio trick and can be approximated using Monte Carlo sampling.

Step 4: Update the Policy Parameters

Update the policy parameters using gradient ascent to maximize the policy gradient. Common optimization algorithms like stochastic gradient ascent or Adam are used to update the parameters.

Example of Policy Gradients

Let's illustrate how to implement a simple policy gradient agent to play the game CartPole using Python and the popular deep learning library TensorFlow.


    import gym
    import numpy as np
    import tensorflow as tf
    from tensorflow.keras.layers import Dense
    from tensorflow.keras.optimizers import Adam

    # Create the policy network
    model = tf.keras.Sequential([
        Dense(24, input_shape=(4,), activation='relu'),
        Dense(24, activation='relu'),
        Dense(2, activation='softmax')
    ])

    optimizer = Adam(learning_rate=0.001)

    # Environment setup
    env = gym.make('CartPole-v1')

    # Policy Gradient parameters
    num_episodes = 1000
    gamma = 0.99

    def compute_discounted_rewards(rewards):
        discounted_rewards = np.zeros_like(rewards)
        cumulative_reward = 0
        for t in reversed(range(len(rewards))):
            cumulative_reward = cumulative_reward * gamma + rewards[t]
            discounted_rewards[t] = cumulative_reward
        return discounted_rewards

    for episode in range(num_episodes):
        state = env.reset()
        rewards = []
        actions = []
        states = []

        for time_step in range(500):
            state = np.reshape(state, [1, 4])
            action_probs = model.predict(state)[0]
            action = np.random.choice(len(action_probs), p=action_probs)
            next_state, reward, done, _ = env.step(action)

            states.append(state)
            actions.append(action)
            rewards.append(reward)

            state = next_state

            if done:
                break

        discounted_rewards = compute_discounted_rewards(rewards)
        states = np.vstack(states)
        actions = np.array(actions)

        with tf.GradientTape() as tape:
            action_probs = model(states, training=True)
            chosen_action_probs = tf.reduce_sum(tf.one_hot(actions, env.action_space.n) * action_probs, axis=1)
            log_probs = tf.math.log(chosen_action_probs)
            loss = -tf.reduce_mean(log_probs * discounted_rewards)

        grads = tape.gradient(loss, model.trainable_variables)
        optimizer.apply_gradients(zip(grads, model.trainable_variables))

Common Mistakes with Policy Gradients

Using a high learning rate, which can lead to unstable training and hinder convergence.
Not properly normalizing the advantages when computing the policy gradient, resulting in biased or suboptimal updates.
Using a policy network with insufficient capacity to represent the optimal policy, leading to poor performance.

Frequently Asked Questions (FAQs)

Q: Can policy gradients handle discrete action spaces?
A: Yes, policy gradients can handle both discrete and continuous action spaces by choosing an appropriate policy parametrization.
Q: How can I choose the policy network architecture for policy gradients?
A: The choice of architecture depends on the complexity of the environment and the problem. For continuous action spaces, Gaussian policies with a neural network are common, while softmax policies are used for discrete action spaces.
Q: Are policy gradients more suitable for episodic or continuing tasks?
A: Policy gradients can be used for both episodic and continuing tasks. For episodic tasks, the agent collects trajectories and updates the policy after each episode. For continuing tasks, the agent updates the policy during online interactions with the environment.
Q: How can I deal with high variance in policy gradients?
A: High variance can be addressed by using techniques like reward scaling, baseline subtraction, or implementing more advanced algorithms like Proximal Policy Optimization (PPO).
Q: Can policy gradients handle environments with delayed rewards?
A: Yes, policy gradients can handle environments with delayed rewards. The discounted rewards used in policy gradients account for long-term cumulative rewards.

Summary

Policy gradients are powerful algorithms in reinforcement learning that directly learn policies to maximize cumulative rewards. These algorithms are particularly useful for tasks with continuous action spaces and offer great flexibility in optimizing complex policies. By understanding the steps involved in implementing policy gradients and avoiding common mistakes, you can effectively apply this approach to a wide range of reinforcement learning problems, enabling intelligent decision-making in artificial neural networks.