Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds

Zhe Cheng, Fode Zhang, Yifan Zhu, Lingrui Wang, Jiaolong Wang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:19145-19178, 2026.

Abstract

We study unsupervised domain adaptation (UDA) where measuring cross-domain discrepancy is critical. Most UDA approaches fix a single $f$-divergence a priori, which can be suboptimal across heterogeneous shifts. We propose a framework that (i) tightens the variational lower bound of an $f$-divergence by inserting a learnable, monotone $L$-Lipschitz transform $\tau$ (Tighter-VR), and (ii) selects the divergence family adaptively from data via a likelihood-based criterion. The resulting estimator yields more informative and statistically efficient discrepancy estimates while recovering prior fixed-divergence methods as special cases. Theoretically, we derive a target-risk bound whose three components are a transformed source risk, a Tighter-VR discrepancy between domains, and an ideal-hypothesis residual; we further provide finite-sample guarantees using standard complexity measures. Empirically, on Office-31, Office-Home, Digits, and VisDA-2017, our method consistently improves accuracy over strong baselines, showing that coupling Tighter-VR with adaptive divergence selection is useful for UDA.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-cheng26r, title = {Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds}, author = {Cheng, Zhe and Zhang, Fode and Zhu, Yifan and Wang, Lingrui and Wang, Jiaolong}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {19145--19178}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/cheng26r/cheng26r.pdf}, url = {https://proceedings.mlr.press/v306/cheng26r.html}, abstract = {We study unsupervised domain adaptation (UDA) where measuring cross-domain discrepancy is critical. Most UDA approaches fix a single $f$-divergence a priori, which can be suboptimal across heterogeneous shifts. We propose a framework that (i) tightens the variational lower bound of an $f$-divergence by inserting a learnable, monotone $L$-Lipschitz transform $\tau$ (Tighter-VR), and (ii) selects the divergence family adaptively from data via a likelihood-based criterion. The resulting estimator yields more informative and statistically efficient discrepancy estimates while recovering prior fixed-divergence methods as special cases. Theoretically, we derive a target-risk bound whose three components are a transformed source risk, a Tighter-VR discrepancy between domains, and an ideal-hypothesis residual; we further provide finite-sample guarantees using standard complexity measures. Empirically, on Office-31, Office-Home, Digits, and VisDA-2017, our method consistently improves accuracy over strong baselines, showing that coupling Tighter-VR with adaptive divergence selection is useful for UDA.} }
Endnote
%0 Conference Paper %T Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds %A Zhe Cheng %A Fode Zhang %A Yifan Zhu %A Lingrui Wang %A Jiaolong Wang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-cheng26r %I PMLR %P 19145--19178 %U https://proceedings.mlr.press/v306/cheng26r.html %V 306 %X We study unsupervised domain adaptation (UDA) where measuring cross-domain discrepancy is critical. Most UDA approaches fix a single $f$-divergence a priori, which can be suboptimal across heterogeneous shifts. We propose a framework that (i) tightens the variational lower bound of an $f$-divergence by inserting a learnable, monotone $L$-Lipschitz transform $\tau$ (Tighter-VR), and (ii) selects the divergence family adaptively from data via a likelihood-based criterion. The resulting estimator yields more informative and statistically efficient discrepancy estimates while recovering prior fixed-divergence methods as special cases. Theoretically, we derive a target-risk bound whose three components are a transformed source risk, a Tighter-VR discrepancy between domains, and an ideal-hypothesis residual; we further provide finite-sample guarantees using standard complexity measures. Empirically, on Office-31, Office-Home, Digits, and VisDA-2017, our method consistently improves accuracy over strong baselines, showing that coupling Tighter-VR with adaptive divergence selection is useful for UDA.
APA
Cheng, Z., Zhang, F., Zhu, Y., Wang, L. & Wang, J.. (2026). Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:19145-19178 Available from https://proceedings.mlr.press/v306/cheng26r.html.

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