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Investigating Monte-Carlo Methods on the Weak Schur Problem

机译：调查弱舒尔问题的Monte-Carlo方法

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Nested Monte-Carlo Search (NMC) and Nested Rollout Policy Adaptation (NRPA) are Monte-Carlo tree search algorithms that have proved their efficiency at solving one-player game problems, such as morpion solitaire or sudoku 16x16, showing that these heuristics could potentially be applied to constraint problems. In the field of Ramsey theory, the weak Schur number WS(k) is the largest integer n for which their exists a partition into k subsets of the integers [1, n] such that there is no x < y < z all in the same subset with x+y = z. Several studies have tackled the search for better lower bounds for the Weak Schur numbers WS(k), k ≥ 4. In this paper we investigate this problem using NMC and NRPA, and obtain a new lower bound for WS(6), namely WS(6) ≥ 582.
机译：嵌套Monte-Carlo搜索（NMC）和嵌套卷展策略适应（NRPA）是Monte-Carlo树搜索算法，这些算法已经证明了他们在解决一个玩家游戏问题，例如Morpion Solitaire或Sudoku 16x16，表明这些启发式可能是可能的适用于约束问题。在Ramsey理论的领域中，弱Schur编号WS（k）是它们存在于整数[1，n]的k子集中的分区的最大整数n，使得在其中没有x

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