A Dynamical Systems Approach for Static Evaluation in Go

Abstract--In the paper arguments are given why the concept of static evaluation has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling static evaluation through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated. The concept of Monte-Carlo simulations applied to Go [1] combined with the UCT algorithm [2], [3], which is a tree search method based on Upper Confidence Bounds (UCB) (see e.g. The detailed tournament report [8] of the program MoGo playing against professional and amateur players reveals strengths and weaknesses of MoGo which are typical for programs that perform a Monte Carlo tree search (MCTS). Programs performing MCTS can utilize ever increasing computing power but in their pure form without extra Go knowledge the ratio log(increase in needed computing power) / (increase in strength) is too big to get to professional strength on large boards in the foreseeable future. Therefore in recent years Go knowledge has been incorporated either in form of heuristics, or pattern databases learned from professional games or from self-play. Although treesearch was naturally slowed down the playing strength increased further. With all of this tremendous progress of MCTS compared to the knowledge based era of computer Go summarized in [9], [10], [11], it needs good reasons to start work on a static evaluation function (SE) in Go. One indicator that more Go knowledge needs to be added is that, compared with human playing strength the playing level of current programs decreases as board size increases from 9 9 to 13 13 and then to 19 19. The principal difficulties of deriving knowledge and applying it become more relevant as knowledge is increasingly used in MCTS. Knowledge that is not 100% accurate reduces the scalability of the program when enough computing power is available for global search to replace increasingly the approximate Go knowledge which then becomes less useful or even less accurate than knowledge coming from search. It is difficult to combine knowledge on a high level if it comes from different sources, like from pattern and from local searches. It is one of the reasons of the originally surprising success of pure MCTS that it only uses knowledge from one source (statistics of simulations) without the need of merging different types of knowledge.