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We theoretically demonstrate that existing DR methods face high or even unbounded bias, variance, and generalization error bound under small propensity scores from sparse click events. This motivates us to propose a new Batch-Adaptive DR (BADR) Learning method. In particular, we propose a BADR estimator, which adaptively adjusts the influence of each data batch during debiasing CVR prediction model training based on the propensity scores within that batch. We prove that the BADR estimator has bounded bias, variance, and generalization error bound, all of which are smaller than those of the DR estimator under small propensity scores, while maintaining asymptotic double robustness, i.e., achieving double robustness under a large sample size. Furthermore, we approximate the variance of the BADR estimator and derive a new batch-adaptive imputation model training loss compatible with the BADR estimator, which theoretically ensures further variance reduction during training. Our experiments on real-world datasets validate BADR\u2019s effectiveness and rationality.<\/jats:p>","DOI":"10.1145\/3785146","type":"journal-article","created":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T14:48:22Z","timestamp":1765896502000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Batch-Adaptive Doubly Robust Learning for Debiasing Post-Click Conversion Rate Prediction Under Sparse Data"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8020-203X","authenticated-orcid":false,"given":"Hang","family":"Pan","sequence":"first","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0306-7310","authenticated-orcid":false,"given":"Chunyuan","family":"Zheng","sequence":"additional","affiliation":[{"name":"Peking University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5199-1428","authenticated-orcid":false,"given":"Wenjie","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3713-6865","authenticated-orcid":false,"given":"Jingang","family":"Jiang","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3699-0697","authenticated-orcid":false,"given":"Xueying","family":"Li","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3620-3769","authenticated-orcid":false,"given":"Haoxuan","family":"Li","sequence":"additional","affiliation":[{"name":"Peking University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5828-9842","authenticated-orcid":false,"given":"Fuli","family":"Feng","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,2,16]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/3292500.3330701"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/3404835.3462919"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/3564284"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/2988450.2988454"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/3534678.3539270"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/3534678.3539240"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/3511808.3557220"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/3639048"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2017\/239"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1145\/3404835.3462917"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/3447548.3467384"},{"key":"e_1_3_2_13_2","first-page":"104010","volume-title":"NeurIPS","author":"Ha Mingming","year":"2024","unstructured":"Mingming Ha, Xuewen Tao, Wenfang Lin, Qionxu Ma, Wujiang Xu, and Linxun Chen. 2024. 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