Joint Value Estimation and Bidding in Repeated First-Price Auctions

TL;DR

This paper develops algorithms for repeated first-price auctions that minimize regret by jointly estimating values and optimizing bids, incorporating causal inference and handling different feedback types.

Contribution

It introduces a novel framework combining causal inference with bid optimization in repeated auctions, achieving near-optimal regret bounds without overlap assumptions.

Findings

Algorithms achieve near-optimal regret bounds.

Framework handles full-information and binary feedback.

Eliminates overlap condition in causal inference.

Abstract

We study regret minimization in repeated first-price auctions (FPAs), where a bidder observes only the realized outcome after each auction -- win or loss. This setup reflects practical scenarios in online display advertising where the actual value of an impression depends on the difference between two potential outcomes, such as clicks or conversion rates, when the auction is won versus lost. We incorporate causal inference into this framework and analyze the challenging case where only the treatment effect admits a simple dependence on observable features. Under this framework, we propose algorithms that jointly estimate private values and optimize bidding strategies under two different feedback types on the highest other bid (HOB): the full-information feedback where the HOB is always revealed, and the binary feedback where the bidder only observes the win-loss indicator. Under both cases, our algorithms are shown to achieve near-optimal regret bounds. Notably, our framework enjoys a unique feature that the treatments are actively chosen, and hence eliminates the need for the overlap condition commonly required in causal inference.