Learning to Bid in Repeated First-Price Auctions with Budgets

TL;DR

This paper introduces a novel algorithm for learning optimal bidding strategies in repeated first-price auctions with budgets, achieving near-optimal regret bounds under different feedback settings, and validated through numerical experiments.

Contribution

It develops a dual-based algorithm for budget management in repeated first-price auctions, extending previous work from second-price to first-price settings with theoretical guarantees.

Findings

Achieves $ ilde{O}( oot{T}rom{})$ regret in full information feedback.

Maintains near-optimal regret with limited feedback under mild assumptions.

Numerical experiments confirm the algorithm's effectiveness.

Abstract

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal $\widetilde{O}(\sqrt{T})$ regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an $\widetilde{O}(\sqrt{T})$ regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.