The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915975810514944 |
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| author | Wen, Yuxiao Hu, Zihao Han, Yanjun Yao, Yuan Zhou, Zhengyuan |
| author_facet | Wen, Yuxiao Hu, Zihao Han, Yanjun Yao, Yuan Zhou, Zhengyuan |
| contents | Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect--the outcome difference between winning and losing the auction--and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_01756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Wen, Yuxiao Hu, Zihao Han, Yanjun Yao, Yuan Zhou, Zhengyuan Computer Science and Game Theory Information Theory Machine Learning Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect--the outcome difference between winning and losing the auction--and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions. |
| title | The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions |
| topic | Computer Science and Game Theory Information Theory Machine Learning |
| url | https://arxiv.org/abs/2605.01756 |