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In this paper, we consider planning in stochastic shortest path (SSP)problems, a subclass of Markov Decision Problems (MDP). We focus on medium-sizeproblems whose state space can be fully enumerated. This problem has numerousimportant applications, such as navigation and planning under uncertainty. Wepropose a new approach for constructing a multi-level hierarchy ofprogressively simpler abstractions of the original problem. Once computed, thehierarchy can be used to speed up planning by first finding a policy for themost abstract level and then recursively refining it into a solution to theoriginal problem. This approach is fully automated and delivers a speed-up oftwo orders of magnitude over a state-of-the-art MDP solver on sample problemswhile returning near-optimal solutions. We also prove theoretical bounds on theloss of solution optimality resulting from the use of abstractions.

Speeding Up Planning in Markov Decision Processes via Automatically Constructed Abstractions