Solving Partially Observable Stochastic Shortest-Path Games

Abstract

We study the two-player zero-sum extension of the partially observable stochastic shortest-path problem where one agent has only partial information about the environment. We formulate this problem as a partially observable stochastic game (POSG): given a set of target states and negative rewards for each transition, the player with imperfect information maximizes the expected undiscounted total reward until a target state is reached. The second player with the perfect information aims for the opposite. We base our formalism on POSGs with one-sided observability (OS-POSGs) and give the following contributions: (1) we introduce a novel heuristic search value iteration algorithm that iteratively solves depth-limited variants of the game, (2) we derive the bound on the depth guaranteeing an arbitrary precision, (3) we propose a novel upper-bound estimation that allows early terminations, and (4) we experimentally evaluate the algorithm on a pursuit-evasion game.