Minimax-Optimal Online Contract Design with Unrestricted Bounded Contracts

2026-09-17

AI Summary

研究在主体仅观察结果而非行动的情况下，通过使用有界结果依赖支付向量设计在线合同，以解决预期利润不连续问题，并提出一种学习策略来减少最坏情况下的学习成本。

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.

Problem

• repeated contract design
• bounded outcome-contingent payments
• minimax regret
• agent's best response
• expected profit discontinuity

Innovation

• minimax regret
• effective-dimension reduction
• revealed preference