Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes (extended version)

TL;DR

This paper introduces pseudo-antichain data structures to improve symblicit algorithms for optimal strategy synthesis in monotonic MDPs, demonstrating efficiency in runtime and memory for practical applications.

Contribution

It presents a novel pseudo-antichain based symblicit algorithm for monotonic MDPs, extending previous symbolic methods with open-source implementations.

Findings

Efficient algorithms for expected mean-payoff and stochastic shortest path.

Promising experimental results in automated planning and LTL synthesis.

Reduced runtime and memory consumption compared to existing methods.

Abstract

When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implementations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption.