Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry
Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits. To overcome these bottlenecks, we propose a Geometry-Aware Monte Carlo Tree Search (MCTS) framework. Our approach strictly enforces geometric constraints through incremental updates to the feasible action space.
- ▪Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limit
- ▪To overcome these bottlenecks, we propose a Geometry-Aware Monte Carlo Tree Search (MCTS) framework.
- ▪Our approach strictly enforces geometric constraints through incremental updates to the feasible action space.
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Computer Science > Artificial Intelligence arXiv:2606.26399 (cs) [Submitted on 24 Jun 2026] Title:Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry Authors:Luoning Zhang, Xu Zhuang, Tianhao Wang, Nathan Kaplan View a PDF of the paper titled Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry, by Luoning Zhang and 3 other authors View PDF HTML (experimental) Abstract:We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
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