Learning Pareto manifolds in high dimensions: How can regularization help?

Tobias Wegel, Filip Kovačević, Alexandru Tifrea, Fanny Yang
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4591-4599, 2025.

Abstract

Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-wegel25a, title = {Learning Pareto manifolds in high dimensions: How can regularization help?}, author = {Wegel, Tobias and Kova{\v{c}}evi{\'c}, Filip and Tifrea, Alexandru and Yang, Fanny}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {4591--4599}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/wegel25a/wegel25a.pdf}, url = {https://proceedings.mlr.press/v258/wegel25a.html}, abstract = {Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs.} }
Endnote
%0 Conference Paper %T Learning Pareto manifolds in high dimensions: How can regularization help? %A Tobias Wegel %A Filip Kovačević %A Alexandru Tifrea %A Fanny Yang %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-wegel25a %I PMLR %P 4591--4599 %U https://proceedings.mlr.press/v258/wegel25a.html %V 258 %X Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs.
APA
Wegel, T., Kovačević, F., Tifrea, A. & Yang, F.. (2025). Learning Pareto manifolds in high dimensions: How can regularization help?. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:4591-4599 Available from https://proceedings.mlr.press/v258/wegel25a.html.

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