Machine Discovery of Comprehensible Strategies for Simple Games Using Meta-interpretive Learning

Abstract

Recently, world-class human players have been outperformed in a number of complex two-person games (Go, Chess, Checkers) by Deep Reinforcement Learning systems. However, the data efficiency of the learning systems is unclear given that they appear to require far more training games to achieve such performance than any human player might experience in a lifetime. In addition, the resulting learned strategies are not in a form which can be communicated to human players. This contrasts to earlier research in Behavioural Cloning in which single-agent skills were machine learned in a symbolic language, facilitating their being taught to human beings. In this paper, we consider Machine Discovery of human-comprehensible strategies for simple two-person games (Noughts-and-Crosses and Hexapawn). One advantage of considering simple games is that there is a tractable approach to calculating minimax regret. We use these games to compare Cumulative Minimax Regret for variants of both standard and deep reinforcement learning against two variants of a new Meta-interpretive Learning system called MIGO. In our experiments, tested variants of both normal and deep reinforcement learning have consistently worse performance (higher cumulative minimax regret) than both variants of MIGO on Noughts-and-Crosses and Hexapawn. In addition, MIGO’s learned rules are relatively easy to comprehend, and are demonstrated to achieve significant transfer learning in both directions between Noughts-and-Crosses and Hexapawn.