通过测度优化学习广告拍卖中的出价遮蔽策略，提升收益。
Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization
- 将出价遮蔽建模为测度空间上的凸优化问题。
- 基于上下文动态调整出价分布，最大化预期盈余。
- 方法可闭式求解，适合实时广告投放场景。
本文提出一种首价拍卖中的出价遮蔽策略，将其建模为测度值优化问题。采用标准参数形式的出价遮蔽，并将问题转化为遮蔽参数联合分布上的凸优化。每次拍卖后，基于数据驱动的能量函数，通过正则化Wasserstein近端更新调整遮蔽参数分布。该能量函数依赖于上下文信息，如发布者/用户属性（域名、广告位类型、设备、位置）。所提算法促使出价分布更多聚焦于高预期盈余区域，即中标概率与价值差距均较大的情形。我们证明该测度值凸优化问题存在闭式解。数值实验验证了方法有效性。
原文摘要 · Abstract (English)
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.
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