Rethinking the Flow-based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective

Zhichao Chen, Zhan Zhuang, Yunfei Teng, Hao Wang, Fangyikang Wang, Zhengnan Li, Tianqiao Liu, Haoxuan Li, Zhouchen Lin
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:18712-18756, 2026.

Abstract

Gradual domain adaptation (GDA) aims to mitigate domain shift by progressively adapting models from the source domain to the target domain via intermediate domains. However, real intermediate domains are often unavailable or ineffective, necessitating the synthesis of intermediate samples. Flow-based models have recently been used for this purpose by interpolating between source and target distributions. Notably, their training typically relies on sample-based log-likelihood estimation, which can discard useful information and thus degrade GDA performance. The key to addressing this limitation is constructing the intermediate domains via samples directly. To this end, we propose an $\underline{\text{E}}$ntropy-regularized $\underline{\text{S}}$emi-dual $\underline{\text{U}}$nbalanced $\underline{\text{O}}$ptimal $\underline{\text{T}}$ransport (E-SUOT) framework to construct intermediate domains. Specifically, we reformulate flow-based GDA as a Lagrangian dual problem and derive an equivalent semi-dual objective that circumvents the need for likelihood estimation. However, the dual problem leads to an unstable min–max training procedure. To alleviate this issue, we further introduce the entropy regularization to convert it into a more stable sequential optimization procedure. Based on this, we propose a novel GDA training framework and provide theoretical analysis in terms of stability and generalization. Finally, extensive experiments are conducted to demonstrate the efficacy of the E-SUOT framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26hd, title = {Rethinking the Flow-based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective}, author = {Chen, Zhichao and Zhuang, Zhan and Teng, Yunfei and Wang, Hao and Wang, Fangyikang and Li, Zhengnan and Liu, Tianqiao and Li, Haoxuan and Lin, Zhouchen}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {18712--18756}, 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/chen26hd/chen26hd.pdf}, url = {https://proceedings.mlr.press/v306/chen26hd.html}, abstract = {Gradual domain adaptation (GDA) aims to mitigate domain shift by progressively adapting models from the source domain to the target domain via intermediate domains. However, real intermediate domains are often unavailable or ineffective, necessitating the synthesis of intermediate samples. Flow-based models have recently been used for this purpose by interpolating between source and target distributions. Notably, their training typically relies on sample-based log-likelihood estimation, which can discard useful information and thus degrade GDA performance. The key to addressing this limitation is constructing the intermediate domains via samples directly. To this end, we propose an $\underline{\text{E}}$ntropy-regularized $\underline{\text{S}}$emi-dual $\underline{\text{U}}$nbalanced $\underline{\text{O}}$ptimal $\underline{\text{T}}$ransport (E-SUOT) framework to construct intermediate domains. Specifically, we reformulate flow-based GDA as a Lagrangian dual problem and derive an equivalent semi-dual objective that circumvents the need for likelihood estimation. However, the dual problem leads to an unstable min–max training procedure. To alleviate this issue, we further introduce the entropy regularization to convert it into a more stable sequential optimization procedure. Based on this, we propose a novel GDA training framework and provide theoretical analysis in terms of stability and generalization. Finally, extensive experiments are conducted to demonstrate the efficacy of the E-SUOT framework.} }
Endnote
%0 Conference Paper %T Rethinking the Flow-based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective %A Zhichao Chen %A Zhan Zhuang %A Yunfei Teng %A Hao Wang %A Fangyikang Wang %A Zhengnan Li %A Tianqiao Liu %A Haoxuan Li %A Zhouchen Lin %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-chen26hd %I PMLR %P 18712--18756 %U https://proceedings.mlr.press/v306/chen26hd.html %V 306 %X Gradual domain adaptation (GDA) aims to mitigate domain shift by progressively adapting models from the source domain to the target domain via intermediate domains. However, real intermediate domains are often unavailable or ineffective, necessitating the synthesis of intermediate samples. Flow-based models have recently been used for this purpose by interpolating between source and target distributions. Notably, their training typically relies on sample-based log-likelihood estimation, which can discard useful information and thus degrade GDA performance. The key to addressing this limitation is constructing the intermediate domains via samples directly. To this end, we propose an $\underline{\text{E}}$ntropy-regularized $\underline{\text{S}}$emi-dual $\underline{\text{U}}$nbalanced $\underline{\text{O}}$ptimal $\underline{\text{T}}$ransport (E-SUOT) framework to construct intermediate domains. Specifically, we reformulate flow-based GDA as a Lagrangian dual problem and derive an equivalent semi-dual objective that circumvents the need for likelihood estimation. However, the dual problem leads to an unstable min–max training procedure. To alleviate this issue, we further introduce the entropy regularization to convert it into a more stable sequential optimization procedure. Based on this, we propose a novel GDA training framework and provide theoretical analysis in terms of stability and generalization. Finally, extensive experiments are conducted to demonstrate the efficacy of the E-SUOT framework.
APA
Chen, Z., Zhuang, Z., Teng, Y., Wang, H., Wang, F., Li, Z., Liu, T., Li, H. & Lin, Z.. (2026). Rethinking the Flow-based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:18712-18756 Available from https://proceedings.mlr.press/v306/chen26hd.html.

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