Learning in Online Principal-Agent Interactions: The Power of Menus

TL;DR

This paper introduces a novel approach to online principal-agent problems by allowing the principal to offer menus of strategies, enabling improved learning of the agent's private information and enhancing decision-making in various design settings.

Contribution

It extends existing models by incorporating menus of strategies, providing new algorithms and sample complexity analyses for multiple principal-agent problem variants.

Findings

Developed algorithms with proven sample complexity bounds

Applied framework to Stackelberg games, contract, and information design

Overcame a key hard instance in existing online learning results

Abstract

We study a ubiquitous learning challenge in online principal-agent problems during which the principal learns the agent's private information from the agent's revealed preferences in historical interactions. This paradigm includes important special cases such as pricing and contract design, which have been widely studied in recent literature. However, existing work considers the case where the principal can only choose a single strategy at every round to interact with the agent and then observe the agent's revealed preference through their actions. In this paper, we extend this line of study to allow the principal to offer a menu of strategies to the agent and learn additionally from observing the agent's selection from the menu. We provide a thorough investigation of several online principal-agent problem settings and characterize their sample complexities, accompanied by the corresponding algorithms we have developed. We instantiate this paradigm to several important design problems $-$ including Stackelberg (security) games, contract design, and information design. Finally, we also explore the connection between our findings and existing results about online learning in Stackelberg games, and we offer a solution that can overcome a key hard instance of Peng et al. (2019).