Coevolutionary CMA-ES for Knowledge-Free Learning of Game Position Evaluation

Abstract

One weakness of coevolutionary algorithms observed in knowledge-free learning of strategies for adversarial games has been their poor scalability with respect to the number of parameters to learn. In this paper, we investigate to what extent this problem can be mitigated by using Covariance Matrix Adaptation Evolution Strategy, a powerful continuous optimization algorithm. In particular, we employ this algorithm in a competitive coevolutionary setup, denoting this setting as Co-CMA-ES. We apply it to learn position evaluation functions for the game of Othello and find out that, in contrast to plain (co)evolution strategies, Co-CMA-ES learns faster, finds superior game-playing strategies and scales better. Its advantages come out into the open especially for large parameter spaces of tens of hundreds of dimensions. For Othello, combining Co-CMA-ES with experimentally-tuned derandomized systematic $n$ -tuple networks significantly improved the current state of the art. Our best strategy outperforms all the other Othello 1-ply players published to date by a large margin regardless of whether the round-robin tournament among them involves a fixed set of initial positions or the standard initial position but randomized opponents. These results show a large potential of CMA-ES-driven coevolution, which could be, presumably, exploited also in other games.