Evolving small-board Go players using coevolutionary temporal difference learning with archives

Abstract

We apply Coevolutionary Temporal Difference Learning (CTDL) to learn small-board Go strategies represented as weighted piece counters. CTDL is a randomized learning technique which interweaves two search processes that operate in the intra-game and inter-game mode. Intra-game learning is driven by gradient-descent Temporal Difference Learning (TDL), a reinforcement learning method that updates the board evaluation function according to differences observed between its values for consecutively visited game states. For the inter-game learning component, we provide a coevolutionary algorithm that maintains a sample of strategies and uses the outcomes of games played between them to iteratively modify the probability distribution, according to which new strategies are generated and added to the sample. We analyze CTDL's sensitivity to all important parameters, including the trace decay constant that controls the lookahead horizon of TDL, and the relative intensity of intra-game and inter-game learning. We also investigate how the presence of memory (an archive) affects the search performance, and find out that the archived approach is superior to other techniques considered here and produces strategies that outperform a handcrafted weighted piece counter strategy and simple liberty-based heuristics. This encouraging result can be potentially generalized not only to other strategy representations used for small-board Go, but also to various games and a broader class of problems, because CTDL is generic and does not rely on any problem-specific knowledge.

On Scalability, Generalization, and Hybridization of Coevolutionary Learning: A Case Study for Othello

“…In particular, we investigate how the size of the search space and the type of evaluation function influence the performance of evolutionary, coevolutionary, temporal difference learning (TDL) algorithms, and their hybrids introduced in our previous works [36], [15]. This allows us also to discuss the benefits of global and local search hybridization.…”

Improving coevolution by random sampling

“…Following other studies [16,6], we identify the computational effort with the number of games played in interactions among individuals.…”

Quantitative analysis of the hall of fame coevolutionary archives

“…Even though the archive mechanisms such as the Hall of Fame (HoF) [9,6,5] have been studied in the past and are known to maintain progress in an evolutionary arms race, they do not provide any specific guarantees in terms of convergence to the optimal solution. Moreover, the characteristics of archive's influence on evolving individuals is little known, which constitutes the main motivation for this study.…”