Minimax Regret Optimisation for Robust Planning in Uncertain Markov Decision Processes

TL;DR

This paper introduces a dynamic programming approach using a regret Bellman equation to compute minimax regret-optimal policies in uncertain Markov Decision Processes, especially for stochastic shortest path problems with uncertain costs and transitions.

Contribution

It develops an exact minimax regret optimization method for UMDPs with independent uncertainties and extends it to coupled uncertainties using options.

Findings

Outperforms existing baselines on synthetic domains

Effectively balances computation and solution quality with options

Demonstrates significant robustness in real-world scenarios

Abstract

The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for planning in UMDPs to find robust policies which are not overly conservative. In this work, we focus on planning for Stochastic Shortest Path (SSP) UMDPs with uncertain cost and transition functions. We introduce a Bellman equation to compute the regret for a policy. We propose a dynamic programming algorithm that utilises the regret Bellman equation, and show that it optimises minimax regret exactly for UMDPs with independent uncertainties. For coupled uncertainties, we extend our approach to use options to enable a trade off between computation and solution quality. We evaluate our approach on both synthetic and real-world domains, showing that it significantly outperforms existing baselines.