Mirror Descent Policy Optimisation for Robust Constrained Markov Decision Processes

TL;DR

This paper introduces a mirror descent policy optimization method for robust constrained Markov decision processes, enhancing safety and robustness in reinforcement learning through novel algorithms and theoretical guarantees.

Contribution

It proposes a new mirror descent policy optimization algorithm for robust constrained MDPs, with convergence guarantees and an auxiliary algorithm for adversarial environment design.

Findings

Achieves $ ilde{O}(1/T^{1/3})$ convergence rate.

Demonstrates improved robustness in experiments.

Provides an algorithm for approximate gradient descent in transition kernels.

Abstract

Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under epistemic uncertainty. This paper presents mirror descent policy optimisation for robust constrained Markov decision processes, making use of policy gradient techniques to optimise both the policy (as a maximiser) and the transition kernel (as an adversarial minimiser) on the Lagrangian representing a constrained Markov decision process. Our proposed algorithm obtains an $\tilde{\mathcal{O}}\left(1/T^{1/3}\right)$ convergence rate in the sample-based robust constrained Markov decision process setting. The paper also contributes an algorithm for approximate gradient descent in the space of transition kernels, which is of independent interest for designing adversarial environments in general Markov decision processes. Experiments confirm the benefits of mirror descent policy optimisation in constrained and unconstrained optimisation, and significant improvements are observed in robustness tests when compared to baseline policy optimisation algorithms.