Multiple-Environment Markov Decision Processes

TL;DR

This paper introduces Multi-Environment Markov Decision Processes (MEMDPs), enabling the synthesis of controllers that perform reliably across multiple environments, with some verification problems becoming decidable and more efficient compared to partially observable MDPs.

Contribution

The paper defines MEMDPs and demonstrates that certain verification problems are decidable and can be solved efficiently, unlike in partially observable MDPs.

Findings

Verification problems are decidable for MEMDPs.

Some problems have efficient solutions.

MEMDPs extend the applicability of MDPs in uncertain environments.

Abstract

We introduce Multi-Environment Markov Decision Processes (MEMDPs) which are MDPs with a set of probabilistic transition functions. The goal in a MEMDP is to synthesize a single controller with guaranteed performances against all environments even though the environment is unknown a priori. While MEMDPs can be seen as a special class of partially observable MDPs, we show that several verification problems that are undecidable for partially observable MDPs, are decidable for MEMDPs and sometimes have even efficient solutions.