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This coupling can entangle an integrable component of collective improvement with cyclic interaction dynamics, leading to slow or unstable multi-agent learning. Existing approaches, such as regularization, credit assignment, and consensus methods, stabilize MARL through local or algorithmic modifications; HPML complements them by projecting the joint update field onto a metric-gradient component. We introduce \\textbf{HPML} (\\textbf{H}odge-\\textbf{P}rojected \\textbf{M}ulti-agent \\textbf{L}earning), which views the joint update field of a multi-agent system as an element of an $L^2$ space of vector fields and computes a Hodge-type projection onto the closest metric-gradient potential flow. HPML follows the projected component as the update direction, yielding the closest ","title":"Metric-Gradient Projection for Stable Multi-Agent Policy Learning","url":"https://arxiv.org/abs/2605.18809","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.18809v1 Announce Type: cross \nAbstract: General-sum multi-agent learning is often governed by a stacked update field in which each agent's policy update changes the optimization landscape faced by the others. This coupling can entangle an integrable component of collective improvement with cyclic interaction dynamics, leading to slow or unstable multi-agent learning. Existing approaches, such as regularization, credit assignment, and consensus methods, stabilize MARL through local or algorithmic modifications; HPML complements them by projecting the joint update field onto a metric-gradient component. We introduce \\textbf{HPML} (\\textbf{H}odge-\\textbf{P}rojected \\textbf{M}ulti-agent \\textbf{L}earning), which views the joint update field of a multi-agent system as an element of an $L^2$ space of vector fields and computes a Hodge-type projection onto the closest metric-gradient potential flow. 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