Solving MDPs with LTLf+ and PPLTL+ Temporal Objectives

TL;DR

This paper introduces a novel approach for solving Markov Decision Processes (MDPs) using the expressive temporal logics LTLf+ and PPLTL+, leveraging DFA-based techniques for scalable probabilistic planning.

Contribution

It adapts DFA-based methods for probabilistic systems, enabling efficient, compositional solutions for MDPs with temporal objectives expressed in LTLf+ and PPLTL+.

Findings

Effective in probabilistic systems with controlled nondeterminism

Simpler and more scalable than non-probabilistic approaches

Suitable for symbolic implementation and compositional reasoning

Abstract

The temporal logics LTLf+ and PPLTL+ have recently been proposed to express objectives over infinite traces. These logics are appealing because they match the expressive power of LTL on infinite traces while enabling efficient DFA-based techniques, which have been crucial to the scalability of reactive synthesis and adversarial planning in LTLf and PPLTL over finite traces. In this paper, we demonstrate that these logics are also highly effective in the context of MDPs. Introducing a technique tailored for probabilistic systems, we leverage the benefits of efficient DFA-based methods and compositionality. This approach is simpler than its non-probabilistic counterparts in reactive synthesis and adversarial planning, as it accommodates a controlled form of nondeterminism (``good for MDPs") in the automata when transitioning from finite to infinite traces. Notably, by exploiting compositionality, our solution is both implementation-friendly and well-suited for straightforward symbolic implementations.