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Simplifications to Guide Monte Carlo Tree Search in Combinatorial Games

Michael Haythorpe, Alex Newcombe, Damian O'Dea

TL;DR

The paper addresses guiding Monte Carlo Tree Search in complex combinatorial games by leveraging simplified versions and micro-strategies. It proposes a general metaheuristic that augments MCTS with micro-strategies derived from simplified MB games, forming an ensemble approach. Across three categories of simplifications—board variation, variation of winning sets, and strategy complexity—some instances show preservation of relative performance, enabling efficient identification of promising strategies for the original game. This provides a practical heuristic for strategy development in intractable settings and has potential applications to large-scale Go-like and other combinatorial games.

Abstract

We examine a type of modified Monte Carlo Tree Search (MCTS) for strategising in combinatorial games. The modifications are derived by analysing simplified strategies and simplified versions of the underlying game and then using the results to construct an ensemble-type strategy. We present some instances where relative algorithm performance can be predicted from the results in the simplifications, making the approach useful as a heuristic for developing strategies in highly complex games, especially when simulation-type strategies and comparative analyses are largely intractable.

Simplifications to Guide Monte Carlo Tree Search in Combinatorial Games

TL;DR

The paper addresses guiding Monte Carlo Tree Search in complex combinatorial games by leveraging simplified versions and micro-strategies. It proposes a general metaheuristic that augments MCTS with micro-strategies derived from simplified MB games, forming an ensemble approach. Across three categories of simplifications—board variation, variation of winning sets, and strategy complexity—some instances show preservation of relative performance, enabling efficient identification of promising strategies for the original game. This provides a practical heuristic for strategy development in intractable settings and has potential applications to large-scale Go-like and other combinatorial games.

Abstract

We examine a type of modified Monte Carlo Tree Search (MCTS) for strategising in combinatorial games. The modifications are derived by analysing simplified strategies and simplified versions of the underlying game and then using the results to construct an ensemble-type strategy. We present some instances where relative algorithm performance can be predicted from the results in the simplifications, making the approach useful as a heuristic for developing strategies in highly complex games, especially when simulation-type strategies and comparative analyses are largely intractable.
Paper Structure (7 sections, 1 equation, 3 figures)

This paper contains 7 sections, 1 equation, 3 figures.

Table of Contents

  1. Introduction
  2. Maker Breaker Games
  3. Monte Carlo Tree Search in Games
  4. Micro-Strategies for Weighted MCTS
  5. Types of Game Simplification
  6. Experiments and Discussion
  7. Conclusion

Figures (3)

  • Figure 1: Simulations for three sets of MB games, with Maker win percentage across different parameter values. Different lines correspond to different modified MCTS strategies for Maker and Breaker always uses traditional MCTS. Thick lines are traditional MCTS for Maker. Because the bottom left figure is hard to visualise, the bottom right is an alternative way to make the desired observations.
  • Figure 2: Simulations for two sets of MB games, with Maker win percentage across different parameter values. Different lines correspond to different modified MCTS strategies for Maker and Breaker always uses traditional MCTS. Thick lines are traditional MCTS for Maker. Because the bottom left figure is hard to visualise, the bottom right is an alternative way to make the desired observations.
  • Figure 3: Two sets of MB games, with Maker win percentage across different parameter values. Different lines correspond to different modified MCTS strategies for Maker and Breaker always uses traditional MCTS. Thick lines are traditional MCTS for Maker.