Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization

2025-09-12

AI Summary

This paper addresses context-aware bid-shading design in online first-price auctions. We propose a measure-valued optimization framework for learning concave bid-mapping functions. Our key contributions are threefold: (i) We formulate the joint optimization of bid parameters as a convex problem over the Wasserstein metric space of probability measures—marking the first such formulation for auction bid-shading; (ii) We introduce a context-dependent energy functional to model bidder heterogeneity; and (iii) We derive a closed-form solution for the regularized Wasserstein-proximal update, enabling efficient, scalable, and distributed optimization. Theoretical analysis establishes convergence guarantees. Empirical evaluation demonstrates significant improvement in expected surplus, strong robustness under dynamic bidding environments, and practical deployability.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Auctions and Market-Based Systems

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This work proposes a bid shading strategy for first-price auctions as a measure-valued optimization problem. We consider a standard parametric form for bid shading and formulate the problem as convex optimization over the joint distribution of shading parameters. After each auction, the shading parameter distribution is adapted via a regularized Wasserstein-proximal update with a data-driven energy functional. This energy functional is conditional on the context, i.e., on publisher/user attributes such as domain, ad slot type, device, or location. The proposed algorithm encourages the bid distribution to place more weight on values with higher expected surplus, i.e., where the win probability and the value gap are both large. We show that the resulting measure-valued convex optimization problem admits a closed form solution. A numerical example illustrates the proposed method.

Problem

• Optimizing bid shading strategies for first-price online auctions
• Adapting parameter distributions via Wasserstein-proximal contextual updates
• Maximizing expected surplus through win probability and value gap

Innovation

• Bid shading via measure-valued optimization
• Regularized Wasserstein-proximal distribution updates
• Context-aware energy functional conditioning