Robust Markov Decision Processes: A Place Where AI and Formal Methods Meet

TL;DR

This paper provides a comprehensive tutorial on robust Markov decision processes (RMDPs), explaining their fundamentals, solution methods, and applications in AI and formal methods, highlighting their importance in handling uncertainty in decision-making.

Contribution

It offers a clear, accessible survey of RMDPs, detailing their semantics, solution techniques, and connections to other models, serving as a foundational resource for researchers and practitioners.

Findings

RMDPs extend standard MDPs by incorporating uncertainty sets for transition probabilities.

Value iteration and policy iteration can be adapted to solve RMDPs.

RMDPs are effectively applied in reinforcement learning and abstraction techniques.

Abstract

Markov decision processes (MDPs) are a standard model for sequential decision-making problems and are widely used across many scientific areas, including formal methods and artificial intelligence (AI). MDPs do, however, come with the restrictive assumption that the transition probabilities need to be precisely known. Robust MDPs (RMDPs) overcome this assumption by instead defining the transition probabilities to belong to some uncertainty set. We present a gentle survey on RMDPs, providing a tutorial covering their fundamentals. In particular, we discuss RMDP semantics and how to solve them by extending standard MDP methods such as value iteration and policy iteration. We also discuss how RMDPs relate to other models and how they are used in several contexts, including reinforcement learning and abstraction techniques. We conclude with some challenges for future work on RMDPs.