MCTS Experiments on the Voronoi Game

Abstract

Abstract.Monte-Carlo Tree Search (MCTS) is a powerful tool in games with a finite branching factor. This paper describes an artificial player playing the Voronoi game, a game with an infinite branching factor. First, this paper shows how to use MCTS on a discretization of the Voronoi game, and the effects of enhancements such as RAVE and Gaussian processes (GP). A first set of experimental results shows that MCTS with UCB+RAVE or with UCB+GP are first good solutions for playing the Voronoi game without domain-dependent knowledge. Second, this paper shows how to greatly improve the playing level by using geometrical knowledge about Voronoi diagrams, the balance of diagrams being the key concept. The second set of experimental results shows that a player using MCTS and geometrical knowledge outperforms the player without knowledge.

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

“…For many other application domains the construction of a heuristic evaluation function is an obstacle, too. Therefore we expect that there are many other domains that could benefit from the MCTS technology, and, indeed, many other applications have already been found how to adapt MCTS to fit their characteristics (see, for example, [6,13,28,31,32,40,41,43]). In this paper one such adaptation has been discussed, viz.…”

“…The ability of MCTS to magically home in on clusters of "bright spots" in the state space without relying on domain knowledge has resulted in a long list of other applications, for example, for proofnumber search [40]. In addition, MCTS has been proposed as a new framework for game-AI for video games [13], for the game Settlers of Catan [43], for the game Einstein würfelt nicht [32], for the Voronoi game [6], for Havannah [31], for Amazons [28], and for various single player applications [39,41].…”