Mirror Descent Policy Optimisation for Robust Constrained Markov Decision Processes

• URL: http://arxiv.org/abs/2506.23165v2
• Date: Thu, 25 Sep 2025 13:04:39 GMT
• Title: Mirror Descent Policy Optimisation for Robust Constrained Markov Decision Processes
• Authors: David Bossens, Atsushi Nitanda,
• Abstract summary: This paper presents mirror descent policy optimisation for robust constrained Markov decision processes (RCMDPs)<n>We make 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 MDP.<n> Experiments confirm the benefits of mirror descent policy optimisation in constrained and unconstrained optimisation, and significant improvements are observed in robustness tests.
• Score: 11.162988605397734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 (RCMDPs), 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 MDP. Our proposed algorithm obtains an $\tilde{\mathcal{O}}\left(1/T^{1/3}\right)$ convergence rate in the sample-based RCMDP setting. In addition to the RCMDP 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. 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.

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