A Lazy Abstraction Algorithm for Markov Decision Processes: Theory and Initial Evaluation

TL;DR

A novel lazy abstraction method for MDP analysis based on adaptive simulation graphs that combines a combination of lazy abstraction and Bounded Real-Time Dynamic Programming (BRTDP).

Abstract

Analysis of Markov Decision Processes (MDP) is often hindered by state space explosion. Abstraction is a well-established technique in model checking to mitigate this issue. This paper presents a novel lazy abstraction method for MDP analysis based on adaptive simulation graphs. Refinement is performed only when new parts of the state space are explored, which makes partial exploration techniques like Bounded Real-Time Dynamic Programming (BRTDP) retain more merged states. Therefore, we propose a combination of lazy abstraction and BRTDP. To evaluate the performance of our algorithm, we conduct initial experiments using the Quantitative Verification Benchmark Set.