Improving SAM Requires Rethinking its Optimization Formulation

Wanyun Xie, Fabian Latorre, Kimon Antonakopoulos, Thomas Pethick, Volkan Cevher
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:54475-54487, 2024.

Abstract

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To fundamentally improve this design, we argue that SAM should instead be reformulated using the 0-1 loss. As a continuous relaxation, we follow the simple conventional approach where the minimizing (maximizing) player uses an upper bound (lower bound) surrogate to the 0-1 loss. This leads to a novel formulation of SAM as a bilevel optimization problem, dubbed as BiSAM. BiSAM with newly designed lower-bound surrogate loss indeed constructs stronger perturbation. Through numerical evidence, we show that BiSAM consistently results in improved performance when compared to the original SAM and variants, while enjoying similar computational complexity. Our code is available at https://github.com/LIONS-EPFL/BiSAM.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-xie24d, title = {Improving {SAM} Requires Rethinking its Optimization Formulation}, author = {Xie, Wanyun and Latorre, Fabian and Antonakopoulos, Kimon and Pethick, Thomas and Cevher, Volkan}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {54475--54487}, 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/xie24d/xie24d.pdf}, url = {https://proceedings.mlr.press/v235/xie24d.html}, abstract = {This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To fundamentally improve this design, we argue that SAM should instead be reformulated using the 0-1 loss. As a continuous relaxation, we follow the simple conventional approach where the minimizing (maximizing) player uses an upper bound (lower bound) surrogate to the 0-1 loss. This leads to a novel formulation of SAM as a bilevel optimization problem, dubbed as BiSAM. BiSAM with newly designed lower-bound surrogate loss indeed constructs stronger perturbation. Through numerical evidence, we show that BiSAM consistently results in improved performance when compared to the original SAM and variants, while enjoying similar computational complexity. Our code is available at https://github.com/LIONS-EPFL/BiSAM.} }
Endnote
%0 Conference Paper %T Improving SAM Requires Rethinking its Optimization Formulation %A Wanyun Xie %A Fabian Latorre %A Kimon Antonakopoulos %A Thomas Pethick %A Volkan Cevher %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-xie24d %I PMLR %P 54475--54487 %U https://proceedings.mlr.press/v235/xie24d.html %V 235 %X This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To fundamentally improve this design, we argue that SAM should instead be reformulated using the 0-1 loss. As a continuous relaxation, we follow the simple conventional approach where the minimizing (maximizing) player uses an upper bound (lower bound) surrogate to the 0-1 loss. This leads to a novel formulation of SAM as a bilevel optimization problem, dubbed as BiSAM. BiSAM with newly designed lower-bound surrogate loss indeed constructs stronger perturbation. Through numerical evidence, we show that BiSAM consistently results in improved performance when compared to the original SAM and variants, while enjoying similar computational complexity. Our code is available at https://github.com/LIONS-EPFL/BiSAM.
APA
Xie, W., Latorre, F., Antonakopoulos, K., Pethick, T. & Cevher, V.. (2024). Improving SAM Requires Rethinking its Optimization Formulation. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:54475-54487 Available from https://proceedings.mlr.press/v235/xie24d.html.

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