Probabilistically Robust Learning: Balancing Average and Worst-case Performance

Alexander Robey, Luiz Chamon, George J. Pappas, Hamed Hassani
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:18667-18686, 2022.

Abstract

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness. Our code is available at: https://github.com/arobey1/advbench.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-robey22a, title = {Probabilistically Robust Learning: Balancing Average and Worst-case Performance}, author = {Robey, Alexander and Chamon, Luiz and Pappas, George J. and Hassani, Hamed}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {18667--18686}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/robey22a/robey22a.pdf}, url = {https://proceedings.mlr.press/v162/robey22a.html}, abstract = {Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness. Our code is available at: https://github.com/arobey1/advbench.} }
Endnote
%0 Conference Paper %T Probabilistically Robust Learning: Balancing Average and Worst-case Performance %A Alexander Robey %A Luiz Chamon %A George J. Pappas %A Hamed Hassani %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-robey22a %I PMLR %P 18667--18686 %U https://proceedings.mlr.press/v162/robey22a.html %V 162 %X Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness. Our code is available at: https://github.com/arobey1/advbench.
APA
Robey, A., Chamon, L., Pappas, G.J. & Hassani, H.. (2022). Probabilistically Robust Learning: Balancing Average and Worst-case Performance. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:18667-18686 Available from https://proceedings.mlr.press/v162/robey22a.html.

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