Monte-Carlo Tree Search (MCTS) is a new best-first search method that started a revolution in the field of Computer Go. Parallelizing MCTS is an important way to increase the strength of any Go program. In this article, we discuss three parallelization methods for MCTS: leaf parallelization, root parallelization,and tree parallelization. To be effective tree parallelization requires two techniques: adequately handling of (1) local mutexes and (2) virtual loss. Experiments in 1313 Go reveal that in the program Mango root parallelization may lead to the best results for a specific time setting and specific program parame- ters. However, as soon as the selection mechanism is able to handle more adequately the balance of exploitation and exploration, tree paralleliza- tion should have attention too and could become a second choice for parallelizing MCTS. Preliminary experiments on the smaller 99 board provide promising prospects for tree parallelization.

Parallel Monte-Carlo tree search

Abstract Proof-number search (pn-search) is designed for finding the game-theoretical value in game trees. It is based on ideas derived from conspiracy-number search and its variants, such as applied cn-search and αβ-cn search. While in cn-search the purpose is to continue searching until it is unlikely that the minimax value of the root will change, pn-search aims at proving the true value of the root. Therefore, pn-search does not consider interim minimax values. Pn-search selects the next node to be expanded using two criteria: the potential range of subtree values and the number of nodes which must conspire to prove or disprove that range of potential values. These two criteria enable pn-search to treat efficiently game trees with a non-uniform branching factor. It is shown that in non-uniform trees pn-search outperforms other types of search, such as α-β iterative-deepening search, even when enhanced with transposition tables, move ordering for the full principal variation, etc. Pn-search has been used to establish the game-theoretical values of Connect-Four, Qubic, and Go-Moku. There pn-search was able to find a forced win for the player to move first. The experiments described here are in the domain of Awari, a game which has not yet been solved. The experiments are repeatable for other games with a non-uniform branching factor. This article describes the underlying principles of pn-search, presents an appropriate implementation, and provides an analysis of its strengths and weaknesses.

Proof-Number Search

Df-pn algorithm for searching AND/OR trees and its applications

Solving games is a challenging and attractive task in the domain of Artificial Intelligence. Despite enormous progress, solving increasingly difficult games or game positions continues to pose hard technical challenges. Over the last twenty years, algorithms based on the concept of proof and disproof numbers have become dominating techniques for game solving. Prominent examples include solving the game of checkers to be a draw, and developing checkmate solvers for shogi, which can find mates that take over a thousand moves. This article provides an overview of the research on Proof-Number Search and its many variants and enhancements.

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Game-Tree Search Using Proof Numbers: The First Twenty Years

An approach called generic job-level (JL) search was proposed to solve computer game applications by dispatching jobs to remote workers for parallel processing. This paper applies JL search to alpha-beta search, and proposes a JL alpha-beta search (JL-ABS) algorithm based on a best-first search version of MTD(f). The JL-ABS algorithm is demonstrated by using it in an opening book analysis for Chinese chess. The experimental results demonstrated that JL-ABS reached a speed-up of 10.69 when using 16 workers in the JL system.

Job-Level Alpha-Beta Search

This paper introduces an approach, called generic job-level search, to leverage the game-playing programs which are already written and encapsulated as jobs. Such an approach is well suited to a distributed computing environment, since these jobs are allowed to be run by remote processors independently. In this paper, we present and focus on a job-level proof number search (JL-PNS), a kind of generic job-level search for solving computer game search problems, and apply JL-PNS to solving automatically several Connect6 positions, including some difficult openings. This paper also proposes a method of postponed sibling generation to generate nodes smoothly, and some policies, such as virtual win, virtual loss, virtual equivalence, flagging, or hybrids of the above, to expand the nodes. Our experiment compared these policies, and the results showed that the virtual-equivalence policy, together with flagging, performed the best against other policies. In addition, the results also showed that the speedups for solving these positions are 8.58 on average on 16 cores.

https://ir.nctu.edu.tw:443/bitstream/11536/21399/1/000316479500004.pdf

Po-Ting Chen

Papers

Job-Level Proof Number Search