Dynamic Programming for One-sided Partially Observable Pursuit-evasion Games

Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the players have partial observability, however, the evader has an advantage of knowing the current position of pursuer's units. This setting is particularly interesting for security domains where a robust strategy, maximizing the utility in the worst-case scenario, is often desirable. We provide, to the best of our knowledge, the first algorithm that provably converges to the value of a partially observable pursuit-evasion game with infinite horizon. Our algorithm extends well-known value iteration algorithm by exploiting that (1) value functions of our game depend only on the position of the pursuer and the belief he has about the position of the evader, and (2) that these functions are piecewise linear and convex in the belief space.