在多次出价拍卖中，同时估算价值并优化出价策略。
Joint Value Estimation and Bidding in Repeated First-Price Auctions
- 结合因果推断，通过观测胜负结果反推真实价值
- 两种反馈下均实现近似最优后悔值，含全量与二元反馈
- 主动选择出价策略，无需传统因果推断的重叠假设
我们研究重复第一价格拍卖中的后悔最小化问题，投标者仅能观察每次拍卖的最终结果——胜或败。该设定反映了在线展示广告中的实际场景，其中广告位的真实价值取决于中标与落标时的潜在差异，如点击率或转化率。本文将因果推断引入该框架，并分析仅处理效应与可观测特征存在简单依赖关系的复杂情况。提出算法在两种不同类型的最高他方出价（HOB）反馈下联合估计私有价值并优化出价策略：一种是始终揭示完整HOB的全信息反馈，另一种是仅提供胜/败指示的二元反馈。在两种情况下，所提算法均达到近似最优的后悔界。特别地，本框架具有独特优势：处理（出价）是主动选择的，因此无需因果推断中常见的重叠条件。
原文摘要 · Abstract (English)
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.
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