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Minimax-Optimal Online Contract Design with Unrestricted Bounded Contracts

arXiv · AI, language, vision and robotics · article · Sep 17, 2026 · UTC

We study repeated contract design when a principal observes outcomes but not the actions that generate them. The principal may use any bounded outcome-contingent payment vector, and the agent's best response can make expected profit discontinuous in those payments. For every fixed number $m\ge2$ of outcomes, the minimax regret over $T$ rounds is of order $T^{m/(m+1)}$, up to logarithmic factors. The upper bound allows arbitrary action spaces and agent heterogeneity, without smoothness or monotone-surplus assumptions. Its key is an effective-dimension reduction that the benchmark can be normali

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