Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909821292249088 |
|---|---|
| author | Trillos, Camilo Andrés García Trillos, Nicolás García |
| author_facet | Trillos, Camilo Andrés García Trillos, Nicolás García |
| contents | We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-agnostic robust risk minimization problem. We provide explicit characterizations for important cases such as the cross-entropy loss, loss functions with a power form, and the quadratic loss, extending in this way available results for the 0-1 loss. These reformulations enable efficient computation of sharp lower bounds for adversarial risks and facilitate the design of robust classifiers beyond the 0-1 loss setting. Our paper uncovers interesting connections between adversarial robustness, $α$-fair packing problems, and generalized barycenter problems for arbitrary positive measures where Kullback-Leibler and Tsallis entropies are used as penalties. Our theoretical results are accompanied with illustrative numerical experiments where we obtain tighter lower bounds for adversarial risks with the cross-entropy loss function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions Trillos, Camilo Andrés García Trillos, Nicolás García Machine Learning Optimization and Control We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-agnostic robust risk minimization problem. We provide explicit characterizations for important cases such as the cross-entropy loss, loss functions with a power form, and the quadratic loss, extending in this way available results for the 0-1 loss. These reformulations enable efficient computation of sharp lower bounds for adversarial risks and facilitate the design of robust classifiers beyond the 0-1 loss setting. Our paper uncovers interesting connections between adversarial robustness, $α$-fair packing problems, and generalized barycenter problems for arbitrary positive measures where Kullback-Leibler and Tsallis entropies are used as penalties. Our theoretical results are accompanied with illustrative numerical experiments where we obtain tighter lower bounds for adversarial risks with the cross-entropy loss function. |
| title | Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2510.01969 |