Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements -- defined via a refinement relation inspired by filtrations in probability theory -- lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

翻译：在线广告平台依赖机器学习模型预测点击率（pCTR）和转化率（pCVR）以支持拍卖机制。本文提出一种新颖的理论框架，研究推荐系统模型质量、拍卖格式与自动竞价者行为之间的交互关系。我们形式化定义了模型改进——基于概率论中滤子概念导出的精炼关系——何时能提升平台级评估指标（如收入、社会福利或流动性社会福利）。主要贡献包括：(1) 基于聚类精炼的模型改进形式化定义，(2) 对不同竞价者类型（tCPA、max-CPA）、拍卖格式（一价拍卖、二价拍卖、VCG）及预算约束组合下评估指标单调性的系统性刻画。研究证明：无预算约束的tCPA竞价者在均匀竞价条件下，一价拍卖能确保收入单调性（通过詹森不等式），而二价拍卖与预算约束可能破坏该性质。我们为非单调性结果提供了完整的数值构造。该发现对寻求模型改进与业务成果对齐的广告平台具有实际指导意义。