Using Caching to Solve Larger Probabilistic Planning Problems

Probabilistic planning algorithms seek effective plans for large, stochastic domains. MAXPLAN is a recently developed algorithm that converts a planning problem into an E-MAJSAT problem, an NpPP-complete problem that is essentially a probabilistic version of SAT, and draws on techniques from Boolean satisfiability and dynamic programming to solve the E-MAJSAT problem. This solution method is able to solve planning problems at state-of-the-art speeds, but it depends on the ability to store a value for each CNF subformula encountered in the solution process and is therefore quite memory intensive; searching for moderate-size plans even on simple problems can exhaust memory. This paper presents two techniques, based on caching, that overcome this problem without significant performance degradation. The first technique uses an LRU cache to store a fixed number of subformula values. The second technique uses a heuristic based on a measure of subformula difficulty to selectively save the values of only those subformulas whose values are sufficiently difficult to compute and are likely to be reused later in the solution process. We report results for both techniques on a stochastic test problem.