Checkmating One, by Using Many: Combining Mixture of Experts with MCTS to Improve in Chess
Abstract: In games like chess, strategy evolves dramatically across distinct phases - the opening, middlegame, and endgame each demand different forms of reasoning and decision-making. Yet, many modern chess engines rely on a single neural network to play the entire game uniformly, often missing opportunities to specialize. In this work, we introduce M2CTS, a modular framework that combines Mixture of Experts with Monte Carlo Tree Search to adapt strategy dynamically based on game phase. We explore three different methods for training the neural networks: Separated Learning, Staged Learning, and Weighted Learning. By routing decisions through specialized neural networks trained for each phase, M2CTS improves both computational efficiency and playing strength. In experiments on chess, M2CTS achieves up to +122 Elo over standard single-model baselines and shows promising generalization to multi-agent domains such as Pommerman. These results highlight how modular, phase-aware systems can better align with the structured nature of games and move us closer to human-like behavior in dividing a problem into many smaller units.
- One network fits all? modular versus monolithic task formulations in neural networks. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
- Efficient large scale language modeling with mixtures of experts. In Conference on Empirical Methods in Natural Language Processing, 2021.
- Using reinforcement learning in chess engines. Research in Computing Science, 35:31–40, 2008.
- Rémi Coulom. Efficient selectivity and backup operators in monte-carlo tree search. volume 4630, 05 2006.
- Learning to play the chess variant crazyhouse above world champion level with deep neural networks and human data. Frontiers Artif. Intell., 2020.
- Representation matters: The game of chess poses a challenge to vision transformers, 2023.
- Combining a mixture of experts with transfer learning in complex games. In AAAI Spring Symposia, 2017.
- Glam: Efficient scaling of language models with mixture-of-experts. In ICML, volume 162 of Proceedings of Machine Learning Research, pages 5547–5569. PMLR, 2022.
- Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity. J. Mach. Learn. Res., 23:120:1–120:39, 2022.
- Adaptive mixtures of local experts. Neural Comput., 3(1):79–87, 1991.
- Mixtral of experts, 2024.
- Bandit based monte-carlo planning. In ECML, volume 4212 of Lecture Notes in Computer Science, pages 282–293. Springer, 2006.
- Acquisition of chess knowledge in alphazero. Proceedings of the National Academy of Sciences, 119, 2022.
- Learning models of individual behavior in chess. In Aidong Zhang and Huzefa Rangwala, editors, KDD ’22: The 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, August 14 - 18, 2022, pages 1253–1263, 2022.
- Yu Nasu. Efficiently updatable neural-network-based evaluation functions for computer shogi. The 28th World Computer Shogi Championship Appeal Document, 185, 2018.
- Unveiling concepts learned by a world-class chess-playing agent. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 4864–4872, 2023.
- Scaling vision with sparse mixture of experts. In Marc’Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pages 8583–8595, 2021.
- Mastering atari, go, chess and shogi by planning with a learned model. Nat., 2020.
- Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. In ICLR (Poster). OpenReview.net, 2017.
- A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science, 362(6419), 2018.
- Eca-net: Efficient channel attention for deep convolutional neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11534–11542, 2020.
- Neural network ensembles: combining multiple models for enhanced performance using a multistage approach. Expert Syst. J. Knowl. Eng., 2004.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.