Beyond Monotonicity: Revisiting Factorization Principles in Multi-Agent Q-Learning

• URL: http://arxiv.org/abs/2511.09792v1
• Date: Fri, 14 Nov 2025 01:10:03 GMT
• Title: Beyond Monotonicity: Revisiting Factorization Principles in Multi-Agent Q-Learning
• Authors: Tianmeng Hu, Yongzheng Cui, Rui Tang, Biao Luo, Ke Li,
• Abstract summary: Value decomposition is a central approach in multi-agent reinforcement learning (MARL)<n>Existing methods either enforce monotonicity constraints, which limit expressive power, or adopt softer surrogates at the cost of algorithmic complexity.<n>We show that unconstrained, non-monotonic factorization reliably recovers IGM-optimal solutions and consistently outperforms monotonic baselines.
• Score: 24.476713156225685
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Value decomposition is a central approach in multi-agent reinforcement learning (MARL), enabling centralized training with decentralized execution by factorizing the global value function into local values. To ensure individual-global-max (IGM) consistency, existing methods either enforce monotonicity constraints, which limit expressive power, or adopt softer surrogates at the cost of algorithmic complexity. In this work, we present a dynamical systems analysis of non-monotonic value decomposition, modeling learning dynamics as continuous-time gradient flow. We prove that, under approximately greedy exploration, all zero-loss equilibria violating IGM consistency are unstable saddle points, while only IGM-consistent solutions are stable attractors of the learning dynamics. Extensive experiments on both synthetic matrix games and challenging MARL benchmarks demonstrate that unconstrained, non-monotonic factorization reliably recovers IGM-optimal solutions and consistently outperforms monotonic baselines. Additionally, we investigate the influence of temporal-difference targets and exploration strategies, providing actionable insights for the design of future value-based MARL algorithms.

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