Joint Value Estimation and Bidding in Repeated First-Price Auctions

2025-02-24

AI Summary

This paper studies regret minimization for bidders in repeated first-price auctions with only binary win/lose feedback, modeling real-world online advertising where private values depend on latent outcomes (e.g., click-through rates). We consider three outcome models: featureless adversarial, linear latent outcomes with features, and linear treatment effects. We propose the first online algorithm that jointly models private value estimation and bidding strategy—by actively selecting bids to bypass the overlap assumption in causal inference, and integrating counterfactual reasoning, robust estimation, and hierarchical confidence interval updates for adaptive bidding. Theoretically, our method achieves an $O(sqrt{T})$ near-optimal regret bound under all three settings, strictly improving upon existing decoupled approaches. Ablation studies confirm that joint modeling significantly reduces value estimation bias and increases revenue.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges

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 analyze three outcome models: (1) adversarial outcomes without features, (2) linear potential outcomes with features, and (3) linear treatment effects in features. For each setting, we propose algorithms that jointly estimate private values and optimize bidding strategies, achieving near-optimal regret bounds. Notably, our framework enjoys a unique feature that the treatments are also actively chosen, and hence eliminates the need for the overlap condition commonly required in causal inference.

Problem

• Regret minimization in first-price auctions
• Joint value estimation and bidding strategies
• Eliminating overlap condition in causal inference

Innovation

• Joint value estimation
• Optimized bidding strategies
• Active treatment selection