Value Functions for Depth-Limited Solving in Zero-Sum Imperfect-Information Games
Depth-limited look-ahead search is an essential tool for agents playing perfect-information games. In imperfect information games, the lack of a clear notion of a value of a state makes designing theoretically sound depth-limited solving algorithms substantially more difficult. Furthermore, most results in this direction only consider the domain of poker. We consider two-player zero-sum extensive form games in general. We provide a domain-independent definitions of optimal value functions and prove that they can be used for depth-limited look-ahead game solving. We prove that the minimal set of game states necessary to define the value functions is related to common knowledge of the players. We show the value function may be defined in several structurally different ways. None of them is unique, but the set of possible outputs is convex, which enables approximating the value function by machine learning models.