Overview of the policy gradient method and examples of algorithms and implementations

Overview of the policy gradient method

The Policy Gradient Method is one of the methods in Reinforcement Learning (RL) in which the agent directly learns a policy (a policy for action selection), which uses a probabilistic function of the policy to select actions, By optimising the parameters of that function, it attempts to maximise the agent’s long-term reward.

The main features of the policy gradient method include.

1. policy-based approach: unlike value-based approaches such as Q-learning, the policy gradient method does not use a value function (the value of a state-action pair), but directly optimises the policy (the strategy for selecting an action).

2. probabilistic policy: the agent’s behaviour is selected according to a probability distribution. This can be particularly useful for problems with continuous action spaces and where a variety of strategies are required.

3, gradient updating: the agent updates the parameters of the policy in an ascending gradient fashion, based on the rewards obtained by its actions. The aim is to maximise the expected value of the cumulative reward obtained.

4. balance between exploration and utilisation: probabilistic policies make it easier for agents to maintain a natural balance between exploration (trying out unknown behaviours) and utilisation (choosing known good behaviours).

The policy gradient method takes the following steps.

1. policy definition: the policy for choosing an action \(\pi_{\theta}(a|s)\) represents the probability of choosing action \(a\) for state \(s\) and the policy depends on the parameter \(\theta\).

2. Reward acquisition: the policy is improved based on the reward \(R\) that the agent gets for interacting with the environment.

3. Calculation of the gradient: to update the parameter \(\theta\), the gradient of the expected value of the reward, \(\nabla_{\theta}J(\theta)\), is calculated. This gradient is calculated based on the Policy Gradient Theorem.

4 Policy updating: the policy parameter \(\theta\) is updated using the gradient ascent method (or the inverse of the gradient descent method) to obtain better cumulative rewards.

Typical algorithms for the policy gradient method include

– REINFORCE: the basic algorithm of the policy gradient method, which updates the parameters of the policy based on rewards on an episode-by-episode basis.
– Actor-Critic: a combination of the policy gradient method and the value-based approach, which uses two models – the ‘actor’ and the ‘critic’ – to update the policy. The Critic learns the value function and the Actor improves the policy.

The policy gradient method is a particularly powerful approach for problems with continuous action spaces and high-dimensional state spaces.

Algorithms related to policy gradient methods

Typical algorithms related to policy gradient methods are described below.

1. REINFORCE (Monte Carlo Policy Gradient Method):

– Abstract: REINFORCE, described in ‘Overview of REINFORCE (Monte Carlo Policy Gradient) and examples of algorithms and implementations’, is the most basic policy gradient method, which updates the policy parameters with the accumulated rewards obtained at the end of each episode. REINFORCE updates the parameters with the aim of maximising the expected value of the reward for all episodes.
– Feature:
– Updated based on the results of the entire episode.
– To account for long-term results, the gradient calculation is delayed until the end of the episode.
– Simple method, but can lead to high variability in updates.

2. Actor-Critic method:

– Abstract: Actor-Critic, described in ‘Actor-Critic Overview, Algorithm and Example Implementation’, is a method that combines the policy gradient and value-based methods, where the agent consists of two modules, the ‘actor’ and the ‘critic’. The Actor selects actions according to the policy and the Critic evaluates how good the action was by learning a value function.
– Features:
– No need to wait for episodes (on-policy learning) as the policy is updated in real-time.
– Critiques provide feedback on errors, so that policies can be improved efficiently.
– Typical methods include A3C (Asynchronous Advantage Actor-Critic)**, described in ‘A3C (Asynchronous Advantage Actor-Critic) Overview, Algorithm and Example Implementation’ and **A2C ( Advantage Actor-Critic).

3. Proximal Policy Optimisation (PPO):

– Abstract: PPO, described in ‘Overview of Proximal Policy Optimisation (PPO) and examples of algorithms and implementations’, is an algorithm developed to stabilise the policy gradient method, whereas the conventional policy gradient method sometimes makes learning unstable due to too large updates. However, PPO introduces a constraint called ‘clipping’ to prevent excessive updates.
– Features:
– Stable learning, applicable to many reinforcement learning tasks.
– Faster convergence and higher sample efficiency than other policy gradient methods.
– Model-free and on-policy methods.

4. trust region policy optimisation (TRPO):

– Abstract: TRPO, described in ‘Overview of Trust Region Policy Optimisation (TRPO) and examples of algorithms and implementations’, is a predecessor to PPO, which limits the amount of policy change by KL divergence to avoid excessive policy updates. This method limits the amount of policy change by KL divergence so that policy updates do not become excessive. This prevents excessive updates and policy instability.
– Feature:
– Theoretically guaranteed improvement steps.
– High computational cost.
– More difficult to handle than PPO.

5. Deep Deterministic Policy Gradient (DDPG):

– Abstract: DDPG, described in ‘Overview of Deep Deterministic Policy Gradient (DDPG) and examples of algorithms and implementations’, is an off-policy policy gradient method that operates in a continuous action space, with an Actor-Critic structure, where actors decides on a continuous-valued action, the Critic evaluates the value of the action, and by using an experience playback buffer and a target network, stable learning can be achieved even in off-policy.
– Features:
– Efficiently handles continuous action spaces.
– Experience playback buffer allows data reuse.
– Off-policy methods.

6.Soft Actor-Critic (SAC):

– Abstract: SAC, described in ‘Overview of Soft Actor-Critic (SAC) and examples of algorithms and implementations’, is an off-policy algorithm where agents learn policies while maintaining ‘maximum entropy’ (randomness) in their behaviour selection. This allows the agent to try a variety of behaviours and strike a balance between exploration and exploitation.
– Features:
– Entropy regularisation facilitates exploration and stabilises learning.
– Off-policy method, with good sample efficiency.
– Suitable for continuous action spaces.

Algorithms related to policy gradient methods have different characteristics and can work effectively for different problems. For example, PPO and TRPO are stability-oriented methods, while DDPG and SAC have high performance in continuous action spaces.

Application examples of the policy gradient method

Policy gradient methods are widely used in reinforcement learning, especially in applications such as robotics and game AI. Examples of their application are described below.

1. robotics: policy gradient methods have been effectively used for robots operating in physical environments. In robotics, there are many situations where conventional discrete reinforcement learning methods (e.g. Q-learning) are difficult to apply due to the need to deal with continuous motion spaces and complex operations.

– Robot motion control: policy gradient methods are used in robot arm control, balance control of walking robots and drone flight control, etc. In these systems, continuous torques and angles need to be optimised in real-time for the robot to operate stably, making policy gradient methods is suitable for this purpose.
– Example: drone flight control using Deep Deterministic Policy Gradient (DDPG). Policy gradient methods such as DDPG are effective because they have continuous outputs. 2.

2. game AI: Policy gradient methods are also a powerful technique in complex strategy and action games. In multi-stage scenarios such as games, where long-term reward optimisation is important, policy gradient methods are suitable in many situations.

– AlphaGo: an algorithm that uses part of the policy gradient method and is a case study in beating the world’s best Go players; in AlphaGo, the policy network chooses the next move and the value network evaluates how good the move is.

– AI in Dota 2 and StarCraft II: Policy gradient methods (in particular PPO and A3C) are also used in the development of AI for games, helping to make real-time strategic decisions and optimise continuous actions in the game.

3. autonomous driving: autonomous driving systems need to make optimal route decisions while avoiding obstacles in the environment, making the policy gradient method effective for dealing with continuous operating spaces.

– Vehicle control and path planning: autonomous vehicles need to make continuous decisions such as accelerating, decelerating and changing direction while driving, so the policy gradient method is used to learn the optimal driving policy. For example, proximal policy optimisation (PPO) and soft-actor critiques (SAC) are used.

4. natural language processing (NLP): policy gradient methods have also been applied in the field of natural language processing. In particular, they are used in generative tasks and dialogue systems that utilise reinforcement learning.

– Machine translation: in machine translation, there are cases where a reward function is defined and optimised using the policy gradient method in order to assess the quality of a part of the output. A reward is given based on the quality of the translation result (e.g. BLEU score) and the policy is updated to maximise the reward.

– Dialogue systems: in dialogue systems using reinforcement learning, the policy gradient method is used to learn a policy for generating an optimal response, while receiving user feedback (reward).

5. financial trading: policy gradient methods have also been applied to optimise trading strategies in financial markets. Policy gradient methods are useful in environments such as equity and foreign exchange markets, where the environment is highly uncertain and continuous decisions are required.

– Trading algorithm optimisation: in the design of trading algorithms that buy and sell in response to market conditions, the policy gradient method is used to learn the optimal strategy to obtain maximum returns. This is particularly useful when dealing with continuous actions (e.g. trading volumes).

6. healthcare: policy gradient methods are also used in healthcare to optimise treatment strategies and healthcare systems.

– Individualised treatment planning: policy gradient methods have been applied to systems that adjust treatment policies in real-time based on the patient’s medical condition and treatment effects, learning the optimal policy for treatment while taking into account the different treatment effects for each patient.

Example implementation of the policy gradient method

Examples of basic implementations of policy gradient methods are given in Python. Here, we describe an implementation using one of the simplest policy gradient methods, the REINFORCE algorithm. As a virtual environment, OpenAI’s Gym is used.

1. preparing the environment: first, install the necessary libraries.

pip install gym numpy matplotlib

2. implementation of the REINFORCE algorithm: the following code shows the policy gradient method in a simple environment. The CartPole environment is used here.

import gym
import numpy as np
import matplotlib.pyplot as plt

# policy network
class PolicyNetwork:
    def __init__(self, learning_rate=0.01):
        self.learning_rate = learning_rate
        self.weights = np.random.rand(4)  # Initialise weights according to the number of dimensions of the state.

    def softmax(self, x):
        exp_x = np.exp(x - np.max(x))
        return exp_x / exp_x.sum(axis=0)

    def predict(self, state):
        z = np.dot(self.weights, state)  # Calculate score for status.
        probabilities = self.softmax(z)
        return probabilities

    def update(self, states, actions, rewards):
        # Calculate the gradient for each action and update the weights
        for state, action, reward in zip(states, actions, rewards):
            prob = self.predict(state)
            self.weights += self.learning_rate * (reward - prob[action]) * state

# agent
class REINFORCEAgent:
    def __init__(self):
        self.policy_network = PolicyNetwork()

    def choose_action(self, state):
        probabilities = self.policy_network.predict(state)
        action = np.random.choice(len(probabilities), p=probabilities)
        return action

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

            while not done:
                action = self.choose_action(state)
                new_state, reward, done, _ = env.step(action)

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

                state = new_state

            # Calculate episode rewards and update policy network
            total_reward = sum(rewards)
            rewards_per_episode.append(total_reward)
            self.policy_network.update(states, actions, rewards)

        return rewards_per_episode

# Setting up the environment
env = gym.make('CartPole-v1')
agent = REINFORCEAgent()

# Running the training
num_episodes = 1000
rewards = agent.train(num_episodes)

# Plotting the results
plt.plot(rewards)
plt.xlabel('Episode')
plt.ylabel('Total Reward')
plt.title('REINFORCE on CartPole')
plt.show()

Code description:

1. Policy network: the PolicyNetwork class learns a policy that outputs the probability of an action based on the state and uses the Softmax function to calculate the probability distribution of the action.
2. Agent: the REINFORCEAgent class uses the PolicyNetwork to select actions and update the policy based on feedback from the environment.
3. Training: the train method iterates through the environment for a specified number of episodes and updates the policy network using the rewards obtained from each episode.
4. Plotting the results: finally, the rewards per episode are plotted to visualise the learning progress.

Challenges and measures to address policy gradient methods

Although policy gradient methods are very useful in reinforcement learning, they also pose some challenges. The main challenges and their remedies are described below.

1. high variance: policy gradient methods, especially in Monte Carlo methods such as REINFORCE, can have high reward variance, which makes learning unstable.

– Solution:
– Batch learning: use samples from several episodes at once to update parameters, thus reducing variance.
– Use of reference rewards: reduce reward variance by subtracting the average or reference reward from each episode’s reward.
– Advantage Function: using the value function to calculate an advantage function to make policy updates more stable.

2. low sample efficiency: policy gradient methods may require a large number of samples (episodes) for training and may have low sample efficiency.

– Solution:
– Use of experience replay buffer: samples can be accumulated and reused later to improve learning efficiency (especially with off-policy methods).
– Improved policy: learn more efficiently by using evolved policy gradient methods such as PPO and TRPO.

3. problem of locally optimal solutions: policy gradient methods may converge to a locally optimal solution rather than an optimal solution.

– Solution:
– Different initialisation: try the initial parameters of the policy many times with different values to increase the likelihood of avoiding the local optimum solution.
– Enhanced search strategies: explore a greater variety of behaviours by introducing stochastic action selection and entropy regularisation.

4. computational costs: especially in large environments or with complex policy networks.

– Solution:
– Distributed learning: use computational resources efficiently by training multiple agents in parallel (e.g. A3C).
– Lightweight models: design the size and structure of the model appropriately to increase computational efficiency. 5.

5. reward design: policy gradient methods may not work well when rewards are difficult to design.

– Solution:
– Scaling rewards: adjusting the reward range can help stabilise learning.
– Combined rewards: combining multiple reward signals to clarify the agent’s objectives.

Reference information 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“

“Reinforcement Learning: Theory and Python Implementation“

“Reinforcement Learning: An Introduction (Second Edition)”

“Deep Reinforcement Learning Hands-On”

“Deep Reinforcement Learning with Python”

“Algorithms for Reinforcement Learning”

“Foundations of Deep Reinforcement Learning: Theory and Practice in Python“