Oracle-Efficient Online Learning and Auction Design

TL;DR

This paper introduces oracle-efficient algorithms for online learning and auction design in adversarial settings, achieving near-optimal revenue and regret bounds, and extends these results to various auction types and contextual scenarios.

Contribution

It presents the Generalized Follow-the-Perturbed-Leader algorithm and demonstrates its oracle-efficiency in complex auction environments, addressing open problems in online learning and auction theory.

Findings

Oracle-efficient algorithms achieve vanishing regret in adversarial settings.

Effective auction learning methods for VCG, envy-free pricing, and s-level auctions.

Extension to non-i.i.d. valuation models and contextual learning scenarios.

Abstract

We consider the design of computationally efficient online learning algorithms in an adversarial setting in which the learner has access to an offline optimization oracle. We present an algorithm called Generalized Follow-the-Perturbed-Leader and provide conditions under which it is oracle-efficient while achieving vanishing regret. Our results make significant progress on an open problem raised by Hazan and Koren, who showed that oracle-efficient algorithms do not exist in general and asked whether one can identify properties under which oracle-efficient online learning may be possible. Our auction-design framework considers an auctioneer learning an optimal auction for a sequence of adversarially selected valuations with the goal of achieving revenue that is almost as good as the optimal auction in hindsight, among a class of auctions. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings, (2) envy-free item pricing in multi-item auctions, and (3) s-level auctions of Morgenstern and Roughgarden for single-item settings. The last result leads to an approximation of the overall optimal Myerson auction when bidders' valuations are drawn according to a fast-mixing Markov process, extending prior work that only gave such guarantees for the i.i.d. setting. Finally, we derive various extensions, including: (1) oracle-efficient algorithms for the contextual learning setting in which the learner has access to side information (such as bidder demographics), (2) learning with approximate oracles such as those based on Maximal-in-Range algorithms, and (3) no-regret bidding in simultaneous auctions, resolving an open problem of Daskalakis and Syrgkanis.