Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization
This work addresses bid shading optimization for advertisers in online auctions, presenting an incremental improvement with a novel method for a known bottleneck.
The paper tackles the problem of optimizing bid shading in first-price online auctions by formulating it as a measure-valued convex optimization problem, resulting in a closed-form solution that adapts shading parameters based on context to maximize expected surplus.
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.