PAC–Bayes Guarantees for Data-Adaptive Pairwise Learning
We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statis...
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| Published in | Entropy (Basel, Switzerland) Vol. 27; no. 8; p. 845 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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08.08.2025
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| ISSN | 1099-4300 1099-4300 |
| DOI | 10.3390/e27080845 |
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| Abstract | We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs—a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches—algorithmic stability and PAC–Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n−1/2 under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. |
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| AbstractList | We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs—a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches—algorithmic stability and PAC–Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n[sup.−1/2] under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs—a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches—algorithmic stability and PAC–Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n−1/2 under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs-a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches-algorithmic stability and PAC-Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n-1/2 under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs-a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches-algorithmic stability and PAC-Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n-1/2 under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling.We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs-a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches-algorithmic stability and PAC-Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order n-1/2 under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. |
| Audience | Academic |
| Author | Kabán, Ata Lei, Yunwen Zhou, Sijia |
| AuthorAffiliation | 1 School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK 2 Department of Mathematics, University of Hong Kong, Pokfulam, Hong Hong, China |
| AuthorAffiliation_xml | – name: 2 Department of Mathematics, University of Hong Kong, Pokfulam, Hong Hong, China – name: 1 School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK |
| Author_xml | – sequence: 1 givenname: Sijia orcidid: 0000-0003-2384-6677 surname: Zhou fullname: Zhou, Sijia – sequence: 2 givenname: Yunwen orcidid: 0000-0002-5383-467X surname: Lei fullname: Lei, Yunwen – sequence: 3 givenname: Ata orcidid: 0000-0003-3733-7064 surname: Kabán fullname: Kabán, Ata |
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| Cites_doi | 10.1016/j.neunet.2024.106955 10.1109/TIP.2022.3224325 10.1145/2063576.2063675 10.1109/ICCV.2017.309 10.3390/e23111529 10.21236/ADA623999 10.1038/s42256-024-00876-w 10.1023/A:1007618624809 10.1007/s10444-024-10165-0 10.1007/978-3-642-14267-3 10.1016/j.aei.2024.102972 10.1214/009052607000000910 10.1109/CVPR52688.2022.01489 10.1016/j.inffus.2022.06.006 10.1017/9781108231596 10.1016/j.neucom.2019.12.137 10.1017/CBO9781107298019 10.1145/267460.267466 10.1007/978-3-319-10584-0_1 10.1007/s10994-015-5499-7 10.1109/ICPR.2014.16 10.1109/ICCV.2009.5459197 10.1109/CVPR.2012.6247939 10.1109/TCYB.2019.2959403 |
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| Keywords | algorithmic stability pairwise learning randomized algorithms PAC–Bayes |
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| SubjectTerms | Adaptive sampling algorithmic stability Algorithms Analysis Bayesian analysis Data sampling Design Machine learning Optimization PAC–Bayes pairwise learning Random variables randomized algorithms Statistical methods |
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| Title | PAC–Bayes Guarantees for Data-Adaptive Pairwise Learning |
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