HPML: Hodge-Projected Multi-Agent Learning for Stable Policy Updates

A groundbreaking approach named Hodge-Projected Multi-Agent Learning (HPML) has been introduced to mitigate instability in multi-agent reinforcement learning systems. By projecting joint update fields onto a metric-gradient component, HPML analyzes these fields within an L² space of vector fields. This innovative projection aims to identify the nearest metric-gradient potential flow, effectively directing updates to reduce cyclic interactions that may disrupt learning stability. HPML expands on previous stabilization strategies, including regularization and consensus methods. The full findings can be found in the research paper available on arXiv under the identifier 2605.18809.