Overview of TRPO-CMA and examples of algorithms and implementations

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Overview of the TRPO-CMA

TRPO-CMA (Trust Region Policy Optimization with Covariance Matrix Adaptation) is one of the policy optimization methods in reinforcement learning. It is a combination of TRPO, described in ‘Overview, Algorithms and Implementation Examples of Trust Region Policy Optimisation (TRPO)’, and CMA-ES, described in ‘Overview, Algorithms and Implementation Examples of CMA-ES (Covariance Matrix Adaptation Evolution Strategy)’. This algorithm is designed to efficiently solve complex problems in deep reinforcement learning.

TRPO is a reinforcement learning algorithm based on the policy gradient method, which achieves the following goals

Stable learning: ensuring the stability of the optimisation process by avoiding taking excessive steps during learning.
Constrained updating: updating policies within the constraint of a trust region so that updates are not too large and policies do not change too rapidly.

TRPO updates the policy by solving the following maximisation problem
\[
\max_{\theta} \hat{\mathbb{E}}_t \left[ \frac{\pi_{\theta}(a_t|s_t)}{\pi_{\theta_{\text{old}}}(a_t|s_t)} A_t \right] \] Where \(A_t \) is the advantage of the action, \(\pi_{\theta}\) is the current policy and \(\pi_{\theta_{\text{old}}}\) is the past policy.

This optimisation uses the KL divergence constraint, also described in ‘On the KL divergence constraint’ in TRPO, to prevent sudden changes in policy.

CMA-ES is an evolutionary algorithm, which is mainly used for continuous optimisation problems. It is also one of the evolutionary methods that adaptively adjusts the search space for optimisation.The characteristics of CMA-ES are as follows.

Distributional evolutionary strategy: optimisation proceeds on the basis of a probabilistic distribution rather than a population-based one.
Adaptation of the covariance matrix: adaptively determines the direction of the search and efficiently adjusts the search area.

CMA-ES is a particularly effective approach for black-box and high-dimensional optimisation problems, as it performs search more efficiently in complex continuous spaces.

By combining these two methods, TRPO-CMA aims to obtain the following benefits

Stable policy optimisation: combining TRPO’s constrained optimisation with CMA-ES’s evolutionary search method makes policy updating more efficient and stable. This is particularly effective in complex environments and high-dimensional action spaces.
Effective search space coordination: the CMA-ES adapts the search space and the TRPO provides stable policy updates, facilitating faster convergence to the optimal solution, even in complex environments.
Reinforcement learning accuracy and efficiency: in addition to the stability of the traditional TRPO, the CMA-ES adaptively determines the direction of policy updates, which increases the efficiency of the algorithm and accelerates learning.

Advantages of TRPO-CMA include

Stability: the TRPO’s trust-region constraints prevent unstable updates from occurring during learning.
Efficient search: the covariance matrix adaptation of CMA-ES allows efficient search in high dimensional policy spaces.
Better performance in complex environments: in problems with high-dimensional action spaces and complex state spaces, TRPO-CMA performs better.

implementation example

The basic framework for implementing TRPO-CMA is shown below, where the TRPO and CMA-ES methods are integrated, with CMA-ES used to tune the search space while maintaining the stability of the policy optimisation. This implementation example uses Python’s stable-baselines3 and libraries related to CMA-ES in a reinforcement learning environment.

Installing the necessary libraries

pip install stable-baselines3 gym cma

Implementation example: reinforcement learning with TRPO-CMA

import gym
import numpy as np
from stable_baselines3 import PPO  # Using PPOs in Stable Baselines3
import cma  # Using the CMA-ES

# Configure the environment (e.g. CartPole)
env = gym.make('CartPole-v1')

# Define simple policies (TRPOs often use custom policies)
class CustomPolicy:
    def __init__(self, env):
        self.env = env
        # Set the network structure, initialisation of weights, etc. here.

    def get_action(self, state):
        # Policy calculations.
        action = np.random.choice(self.env.action_space.n)
        return action

# Policy optimisation with CMA-ES
def optimize_with_cma(policy, env, num_generations=50, population_size=10):
    # Initialisation of CMA-ES
    es = cma.CMAEvolutionStrategy(np.random.rand(4), 0.5, {'popsize': population_size})
    
    for gen in range(num_generations):
        # Candidate parameters for new policies by CMA-ES
        solutions = es.ask()
        
        rewards = []
        for sol in solutions:
            # Select actions based on status and calculate rewards in the environment
            total_reward = 0
            for _ in range(10):  # Number of steps per episode.
                state = env.reset()
                done = False
                while not done:
                    action = np.argmax(sol)  # Select actions from the solutions generated by the CMA-ES
                    state, reward, done, _ = env.step(action)
                    total_reward += reward
            rewards.append(total_reward)
        
        # Policies are assessed and updated in the CMA-ES based on compensation
        es.tell(solutions, rewards)
        es.result()  # View results
        
        print(f"Generation {gen} | Best Reward: {max(rewards)}")

    return es.result()

# Running the training
policy = CustomPolicy(env)
optimize_with_cma(policy, env)

Implementation description

Setting up the environment (Gym environment)
- Use the GYM library to create a reinforcement learning environment (CartPole-v1 in this example).
- Use CustomPolicy as a placeholder for defining policies. In practice, the policy network of the TRPO is defined here, but in this case it is simplified and actions are randomly selected as policies.
Optimisation with CMA-ES
- Initialise CMA-ES using the cma library and optimise the parameters of the policy by means of an evolutionary algorithm.
- The optimize_with_cma function uses CMA-ES to evolve the parameters of the policy to improve its performance in the environment.
Calculating rewards and updating the CMA-ES
- The solution generated by the CMA-ES is evaluated and the policy is updated based on the results. The higher the reward, the better the improvement in the next generation.
Training loop
- The algorithm repeats training a specified number of times (num_generations) and uses CMA-ES to optimise the policy.

Improvement points

Building a policy network: TRPOs typically use deep learning as a policy network. As it is simplified here, a stronger policy can be trained by adding a deep network.
Parameter tuning: the parameters (e.g. popsize, num_generations) in the CMA-ES evolutionary search can be tuned to achieve efficient search.

Application examples

TRPO-CMA (Trust Region Policy Optimisation with Covariance Matrix Adaptation) is an algorithm for reinforcement learning, especially when dealing with complex environments and high-dimensional action spaces. Specific application examples are given below.

1. robot control: TRPO-CMA is very effective when controlling the behaviour of robots. In particular, it is used when the environment in which the robot moves is very complex and when dealing with high-dimensional action spaces (e.g. robot arms with multiple joints).

Case study (robot arm action learning): in tasks where the robot arm grabs and moves objects, the action space is very high-dimensional (e.g. the angle of each joint of the robot arm); the stable learning of TRPO combined with the adaptive search by CMA-ES ensures stable policy updates and and optimal movements can be learnt. For example, the robot’s behaviour can be optimised in a changing environment, such as grasping complex objects or avoiding obstacles.
Use case: the TRPO has been successfully used in the OpenAI robot control task and its performance can be improved by using CMA-ES. This can help robots learn to move efficiently while avoiding obstacles.

2. self-driving vehicles: in self-driving vehicle control problems, TRPO-CMA can be used to optimise vehicle manoeuvres (steering, acceleration, braking, etc.). Automated vehicles operate in very complex environments and therefore require great stability in policy updates.

Case study (automated driving in urban areas): automated vehicles driving in the city have to take into account many variables such as vehicle movements, pedestrians, cyclists, other vehicles, etc. Efficient coordination of the search space using CMA-ES and stable policy updates with TRPO can ensure safe and efficient operation. . Different policies can be learnt for motorways and urban areas, e.g. to stably learn the behaviour required when turning at intersections or avoiding obstacles.
Use case: reinforcement learning is used for some vehicle controls in self-driving vehicles such as Waymo and Tesla, and the TRPO-CMA approach is suitable for learning high-dimensional driving behaviour in urban areas.

3. game AI (especially complex strategy games): TRPO-CMA can be applied to AI in real-time strategy games and turn-based games. In these games, agents need to balance long-term strategy with short-term behaviour.

Case study (StarCraft II AI): in highly strategic games such as StarCraft II, the AI needs to take appropriate actions based on complex game situations; TRPO allows it to stabilise and optimise its policies, while CMA-ES allows it to effectively explore strategies. Agents learn complex action spaces, such as resource collection, unit production, combat and map exploration.
Use case: DeepMind’s AlphaStar used reinforcement learning to develop an AI to play StarCraft II; with TRPO-CMA, these strategic decisions could be learnt even more efficiently.

4. multi-agent systems: in multi-agent systems, where multiple agents interact with each other and with the environment, TRPO-CMA can be used to efficiently optimise each agent’s policy. This enables cooperation and conflict between agents to be successfully learnt.

Case study (robot swarm control): when multiple robots cooperate to perform a task, each robot’s behaviour depends on the behaviour of the other robots; by using TRPO-CMA, each robot’s policy can be efficiently learnt and its cooperative or competitive behaviour can be optimised. For example, this can be useful in learning the optimal flight paths and actions in tasks where several drones cooperate to transport an object.
Use case: in Google’s multi-agent system, reinforcement learning is used in scenarios where multiple agents cooperate to complete a task; TRPO-CMA can help to learn efficient cooperative behaviour between these agents.

5. obstacle avoidance in robotics: in tasks where robots reach a target point while avoiding obstacles, TRPO-CMA can be used to optimise the trajectory and actions of the robot.

Case study (autonomous navigation): when a robot reaches its destination while avoiding obstacles, the action space is very large and it is important to optimise the search space: the search space is efficiently adjusted by CMA-ES and stable policy updates are made by TRPO to optimise the Learning movements.
Use case: a robotic cleaner or an autonomous warehouse management robot needs to perform tasks while avoiding obstacles in the environment; TRPO-CMA can be used to efficiently learn obstacle avoidance policies.

TRPO-CMA is a highly effective algorithm when dealing with high-dimensional action spaces and complex environments in reinforcement learning and can be applied to a variety of real-world problems such as robot control, self-driving cars, game AI, multi-agent systems and obstacle avoidance. In particular, it performs well in tasks that require efficient coordination of the search space while maintaining policy stability.

reference book

Reference books for TRPO-CMA (Trust Region Policy Optimisation with Covariance Matrix Adaptation) are listed below.

1. ‘Reinforcement Learning: An Introduction’ (Second Edition) by Richard S. Sutton and Andrew G. Barto
– Abstract: This book provides a comprehensive overview of the fundamentals and applications of reinforcement learning and provides the background knowledge necessary to understand Trust Region Policy Optimisation (TRPO). It will be very useful to deepen understanding of the basic concepts and algorithms of reinforcement learning.
– Relevance: covers the theoretical foundations of the TRPO algorithm.

2. ‘Deep Reinforcement Learning Hands-On: Applying modern RL methods to practical problems of robotics, gaming, and more’ by Maxim Lapan
– Abstract: A practical guide to deep reinforcement learning, with an emphasis on implementation using Python and PyTorch, to learn how to implement TRPO and other reinforcement learning algorithms.
– Relevance: useful for understanding how to implement TRPO and learn to use the algorithms in practice.

3. ‘The CMA Evolution Strategy: A Tutorial’

4. ‘Algorithms for Optimisation’ by Mykel J. Kochenderfer and Tim A. Wheeler
– Abstract: This book introduces the theory and practical solution of optimisation algorithms and provides a detailed study of optimisation methods related to TRPO-CMA. In particular, evolutionary algorithms and stochastic optimisation are mentioned.
– Relevance: knowledge of optimisation algorithms in general is useful for understanding TRPO-CMA.

5. ‘The Art of Reinforcement Learning’ by Marco Wiering and Martijn van Otterlo
– Abstract: The book covers theoretical approaches to reinforcement learning as well as practical methods, with detailed descriptions of different algorithms, including TRPO.
– Relevance: useful for gaining a deep understanding of TRPO and its derived algorithms.

6. ‘Meta-Learning: A Survey’ by Timothée Lesort, Léo D. L. de Lima, and Olivier Pietquin
– Abstract: A review of Meta-Learning, presenting approaches to speeding up and increasing the efficiency of learning using reinforcement learning and evolutionary algorithms.
– Relevance: learn how methods such as TRPO-CMA can be applied in the context of meta-learning.

7. ‘Neural Networks and Deep Learning: A Textbook’ by Charu Aggarwal
– Abstract: A textbook on the theory and practice of deep learning, providing knowledge on the use of deep neural networks in reinforcement learning.
– Relevance: useful for understanding how to combine deep neural networks with policy optimisation algorithms such as TRPO.

8. ‘Evolution Strategies as a Scalable Alternative to Reinforcement Learning’ by Tim Salimans, et al.
– Abstract: A paper describing how evolutionary strategies (ES) can be applied to reinforcement learning, providing an introduction to the theory behind evolutionary approaches such as TRPO-CMA.
– Relevance: a resource for learning the theory behind the evolutionary algorithm part of TRPO-CMA (CMA-ES).

9. ‘Practical Deep Learning for Coders’ by Jeremy Howard and Sylvain Gugger
– Abstract: Practical deep learning book to learn how to implement reinforcement learning algorithms for real-world use; a useful resource for implementing TRPO-CMA algorithms; a good resource for learning the theory of the CMA-ES algorithm; a good resource for learning the theory of the CMA-ES algorithm; a good resource for learning the theory of the CMA-ES algorithm.
– Relevance: to improve your skills in implementing reinforcement learning algorithms while learning the basics of deep learning.

10. ‘Deep Learning for Computer Vision’ by Rajalingappaa Shanmugamani.
– Abstract: This is a computer vision-specific deep learning manual, but also includes reinforcement learning and policy optimisation techniques, and teaches how to apply algorithms such as TRPO to visual tasks.
– Relevance: useful for developing a visual understanding of the application of reinforcement learning algorithms to visual tasks.

– ‘Trust Region Policy Optimisation’ by John Schulman, et al.
– Provides details of TRPO, its background and how it is implemented.