Trust Region Policy Optimization (1502.05477v5)

Abstract: We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

• The paper introduces TRPO, which ensures each policy update improves expected return by optimizing a surrogate objective under a KL divergence constraint.
• It employs both single path and vine sampling schemes to accurately estimate advantages and reduce variance in policy evaluation.
• Empirical results highlight TRPO's robust performance in complex tasks like simulated robotic locomotion and Atari games, demonstrating its scalability.

Trust Region Policy Optimization: A Detailed Overview

Trust Region Policy Optimization (TRPO) is a policy optimization algorithm designed to ensure monotonic improvement in expected return while being scalable to high-dimensional and complex policy representations. The algorithm, proposed by Schulman et al., addresses several limitations of conventional policy gradient and policy iteration methods, especially when dealing with large nonlinear policies, such as those parameterized by neural networks.

Algorithmic Context and Motivation

Reinforcement learning (RL) algorithms for policy optimization generally fall into three broad categories:

• Policy Iteration Methods: These alternate between estimating the value function under the current policy and improving the policy.
• Policy Gradient Methods: These use an estimator of the gradient of the expected return obtained from sample trajectories to update the policy parameters.
• Derivative-Free Optimization Methods: These treat the return as a black-box function to optimize the policy parameters, often using techniques like the cross-entropy method (CEM) and covariance matrix adaptation (CMA).

While derivative-free methods achieve good results on many problems due to their simplicity, gradient-based optimization methods possess better sample complexity guarantees. However, these guarantees often fail to translate into superior performance in practice when applied to high-dimensional control tasks. TRPO aims to bridge this gap by leveraging theoretical insights to design a practical and robust algorithm.

Theoretical Foundations

The theoretical underpinning of TRPO lies in ensuring that each policy update guarantees an improvement in the expected return. Key insights include:

• Surrogate Objective Function: The paper introduces a local approximation to the expected return, denoted as $L_\pi$. This surrogate objective is used to guide the policy updates.
• Trust Region Constraint: To robustly allow large updates, TRPO employs a trust region constraint on the KL divergence between the new and old policies, ensuring that changes in the policy do not deviate excessively from the trusted region.

The main theoretical result shows that maximizing the surrogate objective $L_\pi$ subject to a KL divergence constraint ensures a monotonic improvement in the policy performance. The derivation employs perturbation theory and coupling arguments to bound the difference between the actual expected return and the surrogate objective.

Practical Algorithm

The algorithm can be summarized as follows:

1. Policy Evaluation: Compute advantage estimates for the current policy by sampling trajectories and estimating the $Q$-values.
2. Surrogate Objective Maximization: Solve a constrained optimization problem to maximize the surrogate objective while ensuring that the KL divergence constraint is satisfied.
3. Policy Update: Update the policy parameters based on the solution to the optimization problem.

Two sampling schemes are proposed for estimating the surrogate objective:

• Single Path Sampling: This involves collecting trajectories by simulating the policy and incorporating all state-action pairs into the objective.
• Vine Sampling: This involves constructing a rollout set and performing multiple actions from each state in the rollout set to reduce variance in the advantage estimates.

Numerical Results and Empirical Evaluation

The paper presents extensive empirical evaluations of TRPO on various tasks, demonstrating its robust performance across different domains:

1. Simulated Robotic Locomotion: TRPO is evaluated on complex control tasks involving simulated robotic swimming, hopping, and walking. The results show that TRPO can learn effective control policies for these tasks with minimal tuning of hyperparameters.
2. Atari Games: TRPO is also tested on vision-based RL tasks using raw pixel inputs to play Atari games. Despite the high-dimensional input space and the complexity of the tasks, TRPO achieves competitive performance, demonstrating its scalability and robustness.

Implications and Future Directions

The practical implications of TRPO are significant. The algorithm's scalability and robustness make it applicable to a wide range of challenging RL problems, from continuous control in robotic systems to high-dimensional state spaces in vision-based tasks. The theoretical guarantee of monotonic improvement ensures that the algorithm can be deployed reliably in real-world applications.

Future developments could explore the integration of TRPO with model-based approaches to further reduce sample complexity. Additionally, extending TRPO to handle partially observed environments by incorporating recurrent policies could enhance its applicability to real-world scenarios where full state information is not always available. Combining TRPO with techniques for learning dynamics models could also provide a pathway towards more sample-efficient learning.

In summary, Trust Region Policy Optimization offers a theoretically grounded, practically effective approach to policy optimization in reinforcement learning, and its successful application to diverse and complex tasks underscores its potential as a versatile tool for advancing AI capabilities.