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This paper establishes minimax-optimal regret rates for repeated contract design where the principal learns agent responses from observed outcomes without direct action visibility. By leveraging effective-dimension reduction and Lipschitz parametrization, the authors derive tight bounds that hold even with discontinuous profit functions and arbitrary action spaces. The work provides a theoretical foundation for understanding how incentive compatibility constraints fundamentally limit learning efficiency in multi-outcome environments.
Minimax-Optimal Online Contract Design with Unrestricted Bounded Contracts
arXiv:2609.20353v1 Announce Type: new Abstract: 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 normalized even when fixed tie-breaking is not shift invariant, after which revealed preference yields a monotone response map in payment-difference coordinates. A learning policy built on a Lipschitz parametrization of this map attains the rate using only observed outcome categories. The lower-bound construction accounts for how incentive losses accumulate across outcome dimensions. It shows that each additional contractible outcome creates a precise and unavoidable increase in the worst-case cost of learning.
Abstract: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 normalized even when fixed tie-breaking is not shift invariant, after which revealed preference yields a monotone response map in payment-difference coordinates. A learning policy built on a Lipschitz parametrization of this map attains the rate using only observed outcome categories. The lower-bound construction accounts for how incentive losses accumulate across outcome dimensions. It shows that each additional contractible outcome creates a precise and unavoidable increase in the worst-case cost of learning.
Machine Learning (cs.LG)
arXiv:2609.20353 [cs.LG]
(or arXiv:2609.20353v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.20353 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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