REINFORCE Algorithm

REINFORCE is a policy gradient reinforcement learning algorithm that learns an optimal policy by directly optimizing the probability of selecting actions that maximize the expected cumulative reward. Instead of estimating value functions such as state values or action values, REINFORCE updates the policy parameters using the rewards collected from complete episodes.

Working

1. Collect Episodes: The agent interacts with the environment for a fixed number of steps or until an episode is complete, following the current policy. This generates a trajectory consisting of states, actions and rewards.

2. Calculate Returns: For each time step t, calculate the return G_t​ which is the total reward obtained from time t onwards. Typically, this is the discounted sum of rewards:

G_t = \sum_{k=t}^T \gamma^{k-t}

Where \gamma is the discount factor, T is the final time step of the episode and R_k​ is the reward received at time step k.

3. Policy Gradient Update: The policy parameters θ are updated using the following formula:

\theta_{t+1} = \theta_t + \alpha \nabla_{\theta} \log \pi_{\theta}(a_t | s_t) G_t

Where:

• α is the learning rate.
• \pi_{\theta}(a_t | s_t) is the probability of taking action a_t​ at state s_t, according to the policy.
• G_t is the return or cumulative reward obtained from time step t onwards.
• The gradient \nabla_{\theta} \log \pi_{\theta}(a_t | s_t) represents how much the policy probability for action a_t​ at state s_t should be adjusted based on the obtained return.

4. Repeat: This process is repeated for several episodes, iteratively updating the policy in the direction of higher rewards.

Implementation

In this example we will train a policy network to solve a basic environment such as CartPole from OpenAI's gym. The aim is to use REINFORCE to directly optimize the policy without using value function approximations.

Step 1: Set Up the Environment

The first step is to create the environment using OpenAI's Gym. For this example we use the CartPole-v1 environment where the agent's task is to balance a pole on a cart.

import gym
import numpy as np
import tensorflow as tf
from tensorflow.keras import layers

env = gym.make('CartPole-v1')
obs_space = env.observation_space.shape[0]
act_space = env.action_space.n

Step 2: Define Hyperparameters

In this step we define hyperparameters for the algorithm like discount factor gamma, the learning rate, number of episodes and batch size. These hyperparameters control how the algorithm behaves during training.

gamma = 0.99
learning_rate = 0.01
num_episodes = 1000
batch_size = 64

Step 3: Define the Policy Network (Actor)

We define the policy network as a simple neural network with two dense layers. The input to the network is the state and the output is a probability distribution over the actions (softmax output). The network learns the policy that maps states to action probabilities.

class PolicyNetwork(tf.keras.Model):
    def __init__(self, hidden_units=128):
        super(PolicyNetwork, self).__init__()
        self.dense1 = layers.Dense(hidden_units, activation='relu')
        self.dense2 = layers.Dense(env.action_space.n, activation='softmax')

    def call(self, state):
        x = self.dense1(state)
        return self.dense2(x)

Step 4: Initialize the Policy & Optimizer

Here, we initialize the policy network and the Adam optimizer. The optimizer is used to update the weights of the policy network during training.

policy = PolicyNetwork()
optimizer = tf.keras.optimizers.Adam(learning_rate)

Step 5: Compute Returns

In reinforcement learning, the return G_t is the discounted sum of future rewards. This function computes the return for each time step t, based on the rewards collected during the episode.

def compute_returns(rewards, gamma):
    returns = np.zeros_like(rewards, dtype=np.float32)
    running_return = 0
    for t in reversed(range(len(rewards))):
        running_return = rewards[t] + gamma * running_return
        returns[t] = running_return
    return returns

Step 6: Define Training Step

The training step computes the gradients of the policy network using the log of action probabilities and the computed returns. The loss is the negative log-likelihood of the actions taken, weighted by the return. The optimizer updates the policy network’s parameters to maximize the expected return.

def train_step(states, actions, returns):
    with tf.GradientTape() as tape:
        # Calculate the probability of each action taken
        action_probs = policy(states)
        action_indices = np.array(actions, dtype=np.int32)

        # Gather the probabilities for the actions taken
        action_log_probs = tf.math.log(tf.reduce_sum(
            action_probs * tf.one_hot(action_indices, env.action_space.n), axis=1))

        # Calculate the loss (negative log likelihood * returns)
        loss = -tf.reduce_mean(action_log_probs * returns)

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

Step 7: Training Loop

The training loop collects experiences from episodes and then performs training in batches. The policy is updated after each batch of experiences. In each episode, we record the states, actions and rewards and then compute the returns. The policy is updated based on these returns.

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

    while not done:
        state_input = np.array(state, dtype=np.float32).reshape(1, -1)
        probs = policy(state_input).numpy()[0]
        action = np.random.choice(act_space, p=probs)

        next_state, reward, terminated, truncated, _ = env.step(action)
        done = terminated or truncated

        states.append(state_input[0])
        actions.append(action)
        rewards.append(reward)
        state = next_state

    # After episode ends
    returns = compute_returns(rewards, gamma)
    returns = (returns - np.mean(returns)) / (np.std(returns) + 1e-9)

    states_batch = np.vstack(states)
    train_step(states_batch, actions, returns)

    if episode % 100 == 0:
        print(f"Episode {episode}/{num_episodes}")

Step 8: Testing the Trained Agent

After training the agent, we evaluate its performance by letting it run in the environment without updating the policy. The agent chooses actions based on the highest probabilities (greedy behavior).

state, _ = env.reset()
done = False
total_reward = 0

while not done:
    state_input = np.array(state, dtype=np.float32).reshape(1, -1)
    probs = policy(state_input).numpy()[0]
    action = np.argmax(probs)

    next_state, reward, terminated, truncated, _ = env.step(action)
    done = terminated or truncated
    total_reward += reward
    state = next_state

print(f"Test Total Reward: {total_reward}")

Output:

Episode 0/1000
Episode 100/1000
Episode 200/1000
Episode 300/1000
Episode 400/1000
Episode 500/1000
Episode 600/1000
Episode 700/1000
Episode 800/1000
Episode 900/1000
Test Total Reward: 49.0

You can download the complete code from here.

Variants of REINFORCE Algorithm

Several modifications to the original REINFORCE algorithm have been proposed to address its high variance:

Baseline: By subtracting a baseline value (typically the value function V(s)) from the return G_t​, the variance of the gradient estimate can be reduced without affecting the expected gradient. This results in a variant known as REINFORCE with a baseline.

The update rule becomes:

\theta_{t+1} = \theta_t + \alpha \nabla_{\theta} \log \pi_{\theta}(a_t | s_t) (G_t - b_t)

• Where b_t​ is the baseline such as the expected reward from state s_t​.

Actor-Critic: It is a method that use two parts to learn better: the actor and the critic. The actor chooses what action to take while the critic checks how good that action was and give feedback. This helps to make learning more stable and faster by reducing random mistakes.

Applications

• Robotics: REINFORCE helps robots to learn how to do things like picking up objects or moving around. The robot try different actions and learn from what works well or not.
• Game AI: It is used to teach game players like in video games or board games like chess. The player learns by playing the game many times and figure out what moves led to win.
• Self-driving cars: REINFORCE can help improve how self-driving cars decide to drive safely and efficiently by rewarding good driving decisions.

Advantages

• REINFORCE is simple and easy to use and a good way to start learning about how to improve decision in reinforcement learning.
• It works by directly improving the way actions are chosen which is helpful when there are many possible actions or choices.
• It works well when tasks have a clear finish and the agent gets a total reward at the end.

Challenges

• Policy updates are based on complete episode returns, making learning unstable.
• Requires many interactions with the environment before achieving good performance.
• Learning can take a long time, especially in environments with sparse rewards.
• Since updates occur only after an episode finishes, the algorithm cannot immediately learn from individual actions.

Related Articles

• Reinforcement Learning
• Deep Q-Network (DQN)