On Strength Adjustment for MCTS-Based Programs

Abstract

This paper proposes an approach to strength adjustment for MCTS-based game-playing programs. In this approach, we use a softmax policy with a strength index to choose moves. Most importantly, we filter low quality moves by excluding those that have a lower simulation count than a pre-defined threshold ratio of the maximum simulation count. We perform a theoretical analysis, reaching the result that the adjusted policy is guaranteed to choose moves exceeding a lower bound in strength by using a threshold ratio. The approach is applied to the Go program ELF OpenGo. The experiment results show that is highly correlated to the empirical strength; namely, given a threshold ratio 0.1, z is linearly related to the Elo rating with regression error 47.95 Elo where -2 <= z <= 2. Meanwhile, the covered strength range is about 800 Elo ratings in the interval of in. With the ease of strength adjustment using, we present two methods to adjust strength and predict opponents' strengths dynamically. To our knowledge, this result is state-of-the-art in terms of the range of strengths in Elo rating while maintaining a controllable relationship between the strength and a strength index.