Theoretical Analysis of Heuristic Search Methods for Online POMDPs

Planning in partially observable environments remains a challenging problem, despite significant recent advances in offline approximation techniques. A few online methods have also been proposed recently, and proven to be remarkably scalable, but without the theoretical guarantees of their offline counterparts. Thus it seems natural to try to unify offline and online techniques, preserving the theoretical properties of the former, and exploiting the scalability of the latter. In this paper, we provide theoretical guarantees on an anytime algorithm for POMDPs which aims to reduce the error made by approximate offline value iteration algorithms through the use of an efficient online searching procedure. The algorithm uses search heuristics based on an error analysis of lookahead search, to guide the online search towards reachable beliefs with the most potential to reduce error. We provide a general theorem showing that these search heuristics are admissible, and lead to complete and epsilon-optimal algorithms. This is, to the best of our knowledge, the strongest theoretical result available for online POMDP solution methods. We also provide empirical evidence showing that our approach is also practical, and can find (provably) near-optimal solutions in reasonable time.