Robust Constrained Reinforcement Learning for Handling Model Mismatch

Core Concepts

The goal is to learn a policy that maximizes the worst-case reward while satisfying a constraint on the worst-case utility, even under model mismatch between the training and real environments.

Abstract

The paper addresses the challenge of constrained reinforcement learning (RL) under model mismatch. Existing studies on constrained RL may obtain a well-performing policy in the training environment, but when deployed in a real environment, it may easily violate constraints that were originally satisfied during training due to model mismatch.
To address this challenge, the authors formulate the problem as constrained RL under model uncertainty. The goal is to learn a good policy that optimizes the reward and at the same time satisfies the constraint under model mismatch.
The authors develop a Robust Constrained Policy Optimization (RCPO) algorithm, which is the first algorithm that applies to large/continuous state space and has theoretical guarantees on worst-case reward improvement and constraint violation at each iteration during the training.
The key technical developments include:

A robust performance difference lemma that bounds the difference between the robust value functions of two policies.
A two-step approach that performs policy improvement followed by a projection step to ensure constraint satisfaction.
An efficient approximation for practical implementation of the algorithm.

The authors demonstrate the effectiveness of their algorithm on a set of RL tasks with constraints, including tabular and deep learning cases.

Stats

The paper does not provide any specific numerical data or statistics. It focuses on the theoretical development of the RCPO algorithm and its performance guarantees.

Quotes

"The goal is to learn a good policy that optimizes the reward and at the same time satisfy the constraint under model mismatch."
"Our RCPO algorithm can be applied to large scale problems with a continuous state space."

Key Insights Distilled From

Constrained Reinforcement Learning Under Model Mismatch

by Zhongchang S... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.01327.pdf

Deeper Inquiries

How can the RCPO algorithm be extended to handle multiple constraints simultaneously

To extend the RCPO algorithm to handle multiple constraints simultaneously, we can modify the optimization problem to incorporate all the constraints. Instead of optimizing for a single constraint, we can introduce multiple constraints and ensure that the policy satisfies all of them simultaneously. This can be achieved by adding additional terms to the objective function that penalize violations of each constraint. The optimization problem would then involve maximizing the worst-case reward while ensuring that all constraints are satisfied under model uncertainty. By formulating the problem in this way, the RCPO algorithm can be adapted to handle multiple constraints concurrently.

What are the limitations of the uncertainty set assumption used in this work, and how can it be relaxed or generalized

The uncertainty set assumption used in this work, specifically the (s, a)-rectangularity uncertainty set, has certain limitations. One limitation is that it may not capture all possible sources of model mismatch accurately. To relax or generalize this assumption, we can consider more complex uncertainty sets that allow for a wider range of model variations. For example, we can explore uncertainty sets based on distributional discrepancies or adversarial perturbations to the transition kernels. By incorporating more diverse and realistic uncertainty sets, we can better model the potential model mismatch between the training and real environments.

Can the RCPO framework be applied to other decision-making problems beyond reinforcement learning, such as robust control or robust optimization

The RCPO framework can be applied to other decision-making problems beyond reinforcement learning, such as robust control or robust optimization. In the context of robust control, the RCPO algorithm can be adapted to design controllers that are robust to uncertainties in the system dynamics. By formulating the control problem as a constrained optimization under model uncertainty, the RCPO framework can be used to find control policies that ensure stability and performance guarantees even in the presence of uncertain dynamics. Similarly, in robust optimization, the RCPO algorithm can be utilized to optimize decision-making processes subject to multiple constraints and uncertainties, ensuring robustness and reliability in the face of varying conditions. By extending the RCPO framework to these domains, we can address a wide range of real-world decision-making problems with robustness considerations.