Admissible Distance Heuristics for General Games

Abstract

A general game player is a program that is able to play arbitrary games well given only their rules. One of the main problems of general game playing is the automatic construction of a good evaluation function for these games. Distance features are an important aspect of such an evaluation function, measuring, e.g., the distance of a pawn towards the promotion rank in chess or the distance between Pac-Man and the ghosts.

However, current distance features for General Game Playing are often based on too specific detection patterns to be generally applicable, and they often apply a uniform Manhattan distance regardless of the move patterns of the objects involved. In addition, the existing distance features do not provide proven bounds on the actual distances.

In this paper, we present a method to automatically construct distance heuristics directly from the rules of an arbitrary game. The presented method is not limited to specific game structures, such as Cartesian boards, but applicable to all structures in a game. Constructing the distance heuristics from the game rules ensures that the construction does not depend on the size of the state space, but only on the size of the game description which is exponentially smaller in general. Furthermore, we prove that the constructed distance heuristics are admissible, i.e., provide proven lower bounds on the actual distances.

We demonstrate the effectiveness of our approach by integrating the distance heuristics in an evaluation function of a general game player and comparing the performance with a state-of-the-art player.