Improving SAM Requires Rethinking its Optimization Formulation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917725495885824 |
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| author | Xie, Wanyun Latorre, Fabian Antonakopoulos, Kimon Pethick, Thomas Cevher, Volkan |
| author_facet | Xie, Wanyun Latorre, Fabian Antonakopoulos, Kimon Pethick, Thomas Cevher, Volkan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improving SAM Requires Rethinking its Optimization Formulation Xie, Wanyun Latorre, Fabian Antonakopoulos, Kimon Pethick, Thomas Cevher, Volkan Machine Learning 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. |
| title | Improving SAM Requires Rethinking its Optimization Formulation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.12993 |