Nash Incentive-compatible Online Mechanism Learning via Weakly Differentially Private Online Learning

TL;DR

This paper introduces an incentive-compatible online learning mechanism that combines weakly differentially private algorithms with commitment strategies, achieving low regret in multi-round, adversarial settings without prior knowledge of agent types.

Contribution

It proposes a novel IC online learning framework that integrates privacy and commitment, applicable to general mechanism design beyond auctions, with scalable regret bounds.

Findings

Achieves $O(T^{(1+h)/2})$ regret in adversarial environments.

Ensures incentive compatibility against non-myopic agents.

Applicable to a broad class of mechanism design problems.

Abstract

We study a multi-round mechanism design problem, where we interact with a set of agents over a sequence of rounds. We wish to design an incentive-compatible (IC) online learning scheme to maximize an application-specific objective within a given class of mechanisms, without prior knowledge of the agents' type distributions. Even if each mechanism in this class is IC in a single round, if an algorithm naively chooses from this class on each round, the entire learning process may not be IC against non-myopic buyers who appear over multiple rounds. On each round, our method randomly chooses between the recommendation of a weakly differentially private online learning algorithm (e.g., Hedge), and a commitment mechanism which penalizes non-truthful behavior. Our method is IC and achieves $O(T^{\frac{1+h}{2}})$ regret for the application-specific objective in an adversarial setting, where $h$ quantifies the long-sightedness of the agents. When compared to prior work, our approach is conceptually simpler,it applies to general mechanism design problems (beyond auctions), and its regret scales gracefully with the size of the mechanism class.