Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications

Jiashuo Liu, Jiayun Wu, Tianyu Wang, Hao Zou, Bo Li, Peng Cui
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:32184-32200, 2024.

Abstract

Machine learning algorithms minimizing average risk are susceptible to distributional shifts. Distributionally Robust Optimization (DRO) addresses this issue by optimizing the worst-case risk within an uncertainty set. However, DRO suffers from over-pessimism, leading to low-confidence predictions, poor parameter estimations as well as poor generalization. In this work, we conduct a theoretical analysis of a probable root cause of over-pessimism: excessive focus on noisy samples. To alleviate the impact of noise, we incorporate data geometry into calibration terms in DRO, resulting in our novel Geometry-Calibrated DRO (GCDRO) for regression. We establish the connection between our risk objective and the Helmholtz free energy in statistical physics, and this free-energy-based risk can extend to standard DRO methods. Leveraging gradient flow in Wasserstein space, we develop an approximate minimax optimization algorithm with a bounded error ratio and elucidate how our approach mitigates noisy sample effects. Comprehensive experiments confirm GCDRO’s superiority over conventional DRO methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-liu24br, title = {Geometry-Calibrated {DRO}: Combating Over-Pessimism with Free Energy Implications}, author = {Liu, Jiashuo and Wu, Jiayun and Wang, Tianyu and Zou, Hao and Li, Bo and Cui, Peng}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {32184--32200}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/liu24br/liu24br.pdf}, url = {https://proceedings.mlr.press/v235/liu24br.html}, abstract = {Machine learning algorithms minimizing average risk are susceptible to distributional shifts. Distributionally Robust Optimization (DRO) addresses this issue by optimizing the worst-case risk within an uncertainty set. However, DRO suffers from over-pessimism, leading to low-confidence predictions, poor parameter estimations as well as poor generalization. In this work, we conduct a theoretical analysis of a probable root cause of over-pessimism: excessive focus on noisy samples. To alleviate the impact of noise, we incorporate data geometry into calibration terms in DRO, resulting in our novel Geometry-Calibrated DRO (GCDRO) for regression. We establish the connection between our risk objective and the Helmholtz free energy in statistical physics, and this free-energy-based risk can extend to standard DRO methods. Leveraging gradient flow in Wasserstein space, we develop an approximate minimax optimization algorithm with a bounded error ratio and elucidate how our approach mitigates noisy sample effects. Comprehensive experiments confirm GCDRO’s superiority over conventional DRO methods.} }
Endnote
%0 Conference Paper %T Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications %A Jiashuo Liu %A Jiayun Wu %A Tianyu Wang %A Hao Zou %A Bo Li %A Peng Cui %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-liu24br %I PMLR %P 32184--32200 %U https://proceedings.mlr.press/v235/liu24br.html %V 235 %X Machine learning algorithms minimizing average risk are susceptible to distributional shifts. Distributionally Robust Optimization (DRO) addresses this issue by optimizing the worst-case risk within an uncertainty set. However, DRO suffers from over-pessimism, leading to low-confidence predictions, poor parameter estimations as well as poor generalization. In this work, we conduct a theoretical analysis of a probable root cause of over-pessimism: excessive focus on noisy samples. To alleviate the impact of noise, we incorporate data geometry into calibration terms in DRO, resulting in our novel Geometry-Calibrated DRO (GCDRO) for regression. We establish the connection between our risk objective and the Helmholtz free energy in statistical physics, and this free-energy-based risk can extend to standard DRO methods. Leveraging gradient flow in Wasserstein space, we develop an approximate minimax optimization algorithm with a bounded error ratio and elucidate how our approach mitigates noisy sample effects. Comprehensive experiments confirm GCDRO’s superiority over conventional DRO methods.
APA
Liu, J., Wu, J., Wang, T., Zou, H., Li, B. & Cui, P.. (2024). Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:32184-32200 Available from https://proceedings.mlr.press/v235/liu24br.html.

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