Research in efficient methods for solving infinite-horizon MDPs has so far concentrated primarily on discounted MDPs and the more general stochastic shortest path problems (SSPs). These are MDPs with 1) an optimal value function V*that is the unique solution of Bellman equation and 2) optimal policies that are the greedy policies w.r.t. V*. This paper’s main contribution is the description of a new class of MDPs, that have well-defined optimal solutions that do not comply with either 1 or 2 above. We call our new class Generalized Stochastic Shortest Path (GSSP) problems. GSSP allows more general reward structure than SSP and subsumes several established MDP types including SSP, positive-bounded, negative, and discounted-reward models. While existing efficient heuristic search algorithms like LAO*and LRTDP are not guaranteed to converge to the optimal value function for GSSPs, we present a new heuristic-search-based family of algorithms, FRET (Find, Revise, Eliminate Traps). A preliminary empirical evaluation shows that FRET solves GSSPs much more efficiently than Value Iteration.<\/p>\n","protected":false},"excerpt":{"rendered":"
Research in efficient methods for solving infinite-horizon MDPs has so far concentrated primarily on discounted MDPs and the more general stochastic shortest path problems (SSPs). These are MDPs with 1) an optimal value function V*that is the unique solution of Bellman equation and 2) optimal policies that are the greedy policies w.r.t. V*. 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