Omega-Regular Decision Processes

TL;DR

This paper introduces omega-regular decision processes (ODPs), extending regular decision processes with omega-regular lookaheads, enabling more expressive non-Markovian decision-making with effective optimization and learning methods.

Contribution

The paper proposes omega-regular decision processes (ODPs), extending RDPs with omega-regular lookaheads and providing a reduction to finite MDPs for optimization and learning.

Findings

Effective reduction of ODPs to finite MDPs for optimization.

Experimental validation demonstrating the approach's effectiveness.

Abstract

Regular decision processes (RDPs) are a subclass of non-Markovian decision processes where the transition and reward functions are guarded by some regular property of the past (a lookback). While RDPs enable intuitive and succinct representation of non-Markovian decision processes, their expressive power coincides with finite-state Markov decision processes (MDPs). We introduce omega-regular decision processes (ODPs) where the non-Markovian aspect of the transition and reward functions are extended to an omega-regular lookahead over the system evolution. Semantically, these lookaheads can be considered as promises made by the decision maker or the learning agent about her future behavior. In particular, we assume that, if the promised lookaheads are not met, then the payoff to the decision maker is $\bot$ (least desirable payoff), overriding any rewards collected by the decision maker. We enable optimization and learning for ODPs under the discounted-reward objective by reducing them to lexicographic optimization and learning over finite MDPs. We present experimental results demonstrating the effectiveness of the proposed reduction.