Who Bears the Burden? Learning Responsibility for Shared Constraints in Multi-Agent Reinforcement Learning

arXiv:2610.07491v1 Announce Type: cross Abstract: When multiple agents share a cost budget, a common Lagrange multiplier can enforce the aggregate constraint but does not determine how its penalty should be allocated across agents. Uniform penalties ignore heterogeneity in the rewards agents sacrifice, while agent-specific multipliers may still rely on the same aggregate cost signal. We introduce Lagrangian Responsibility Allocation (LiRA), which learns each agent's share of a common multiplier by optimizing social welfare over a finite training horizon. The multiplier enforces the aggregate b

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