Learning Optimal Contracts: How to Exploit Small Action Spaces

TL;DR

This paper develops an algorithm for learning near-optimal contracts in multi-round principal-agent problems with small action spaces, improving regret bounds and solving an open problem in the field.

Contribution

It introduces a novel algorithm that efficiently learns optimal contracts over multiple rounds when the agent's action space is small, addressing an open problem from prior research.

Findings

Algorithm achieves high-probability near-optimal contract learning in polynomial rounds.

Provides a $ ilde{ ext{O}}(T^{4/5})$ regret bound in online learning setting.

Solves an open problem by Zhu et al. (2022).

Abstract

We study principal-agent problems in which a principal commits to an outcome-dependent payment scheme -- called contract -- in order to induce an agent to take a costly, unobservable action leading to favorable outcomes. We consider a generalization of the classical (single-round) version of the problem in which the principal interacts with the agent by committing to contracts over multiple rounds. The principal has no information about the agent, and they have to learn an optimal contract by only observing the outcome realized at each round. We focus on settings in which the size of the agent's action space is small. We design an algorithm that learns an approximately-optimal contract with high probability in a number of rounds polynomial in the size of the outcome space, when the number of actions is constant. Our algorithm solves an open problem by Zhu et al.[2022]. Moreover, it can also be employed to provide a $\tilde{\mathcal{O}}(T^{4/5})$ regret bound in the related online learning setting in which the principal aims at maximizing their cumulative utility, thus considerably improving previously-known regret bounds.