Monte Carlo Tree Search for Verifying Reachability in Markov Decision Processes

Abstract

The maximum reachability probabilities in a Markov decision process can be computed using value iteration (VI). Recently, simulation-based heuristic extensions of VI have been introduced, such as bounded real-time dynamic programming (BRTDP), which often manage to avoid explicit analysis of the whole state space while preserving guarantees on the computed result. In this paper, we introduce a new class of such heuristics, based on Monte Carlo tree search (MCTS), a technique celebrated in various machine-learning settings. We provide a spectrum of algorithms ranging from MCTS to BRTDP. We evaluate these techniques and show that for larger examples, where VI is no more applicable, our techniques are more broadly applicable than BRTDP with only a minor additional overhead.

A Modest Approach to Markov Automata

“…We are not currently aware of a tool implementation supporting MA in this setting, though. Ashok et al [2] recently showed that MCTS can be combined with the ideas of BRTDP in various ways to obtain different "hybrid" algorithms that provide sound results and perform better than BRTDP alone. MCTS does not apply directly to timed MA settings like checking time-bounded reachability properties due to the need to consider nonmemoryless schedulers.…”