Cartesian Abstractions and Saturated Cost Partitioning in Probabilistic Planning

Abstract

Stochastic shortest path problems (SSPs) capture probabilistic planning tasks with the objective of minimizing expected cost until reaching the goal. One of the strongest methods to solve SSPs optimally is heuristic search guided by an admissible (lower-bounding) heuristic function. Recently, probability-aware pattern database (PDB) abstractions have been highlighted as an efficient way of generating such lower bounds, with significant advantages over traditional determinization-based approaches. Here, we follow this work, yet consider a more general type, Cartesian abstractions, which have been used successfully in the classical setting. We show how to construct probability-aware Cartesian abstractions via a counterexample-guided abstraction refinement (CEGAR) loop akin to classical planning. This method is complete, meaning it guarantees convergence to the optimal expected cost if not terminated prematurely. Furthermore, we investigate the admissible combination of multiple such heuristics using saturated cost partitioning (SCP), marking its first application in the probabilistic setting. In our experiments, we show that probability-aware Cartesian abstractions yield much more informative heuristics than their determinization-based counterparts. Finally, we show that SCP yields probability-aware abstraction heuristics that are superior to the previous state of the art.