Mesh-RL: Coupled subgrid reinforcement learning

• URL: http://arxiv.org/abs/2606.26333v1
• Date: Wed, 24 Jun 2026 19:16:34 GMT
• Title: Mesh-RL: Coupled subgrid reinforcement learning
• Abstract summary: Mesh-RL is a spatial domain-decomposition framework inspired by the finite element method and domain decomposition theory.<n>It partitions the environment into overlapping subgrids and enforces boundary-consistent temporal-difference updates.<n>We evaluate Mesh-RL on hazard-dense grid-world environments with varying geometries and mesh resolutions.
• Score: 0.8192907805418583
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement learning in large or sparse-reward environments suffers from slow temporal-difference reward propagation, as value information spreads only locally across the state space. We propose Mesh-RL, a spatial domain-decomposition framework inspired by the finite element method and domain decomposition theory, which partitions the environment into overlapping subgrids and enforces boundary-consistent temporal-difference updates. Such an approach enables localized learning while ensuring globally coherent value propagation. Unlike hierarchical or model-based approaches, Mesh-RL accelerates long-range credit assignment without modifying the reward function, Bellman operator, or introducing explicit planning mechanisms. We evaluate Mesh-RL on hazard-dense grid-world environments with varying geometries and mesh resolutions. Across Q-learning, SARSA, and Dyna-Q, Mesh-RL consistently improves convergence speed, cumulative reward, and learning stability. Higher mesh resolutions sustain exploration, prevent premature convergence, and substantially accelerate value propagation to distant states. While Dyna-Q already benefits from internal planning, it still achieves additional gains under structured decomposition. Overall, Mesh-RL introduces a principled spatial domain-decomposition mechanism for accelerating temporal-difference learning. Our framework bridges finite element method-inspired boundary-consistency techniques from scientific computing with reinforcement learning to improve sample efficiency in sparse-reward environments. We will release source code of the study.

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