Monte-Carlo Graph Search for AlphaZero

The AlphaZero algorithm has been successfully applied in a range of discrete domains, most notably board games. It utilizes a neural network, that learns a value and policy function to guide the exploration in a Monte-Carlo Tree Search. Although many search improvements have been proposed for Monte-Carlo Tree Search in the past, most of them refer to an older variant of the Upper Confidence bounds for Trees algorithm that does not use a policy for planning. We introduce a new, improved search algorithm for AlphaZero which generalizes the search tree to a directed acyclic graph. This enables information flow across different subtrees and greatly reduces memory consumption. Along with Monte-Carlo Graph Search, we propose a number of further extensions, such as the inclusion of Epsilon-greedy exploration, a revised terminal solver and the integration of domain knowledge as constraints. In our evaluations, we use the CrazyAra engine on chess and crazyhouse as examples to show that these changes bring significant improvements to AlphaZero.