On the existence of solutions to adversarial training in multiclass classification
Adversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting. We prove the existence of Borel measurable robust classifier...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792524000822/type/journal_article |
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| _version_ | 1846143053974208512 |
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| author | Nicolás García Trillos Matt Jacobs Jakwang Kim |
| author_facet | Nicolás García Trillos Matt Jacobs Jakwang Kim |
| author_sort | Nicolás García Trillos |
| collection | DOAJ |
| description | Adversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in their previous work [21]. In addition, we develop new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we provide an alternative proof of the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting. |
| format | Article |
| id | doaj-art-1e19ca8bae5f4116b234a86e846696c4 |
| institution | Kabale University |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-1e19ca8bae5f4116b234a86e846696c42024-12-03T02:52:32ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442512110.1017/S0956792524000822On the existence of solutions to adversarial training in multiclass classificationNicolás García Trillos0Matt Jacobs1Jakwang Kim2Department of Statistics, University of Wisconsin-Madison, Madison, WI, USADepartment of Mathematics, UC Santa Barbara, Santa Barbara, CA, USADepartment of Mathematics, University of British Columbia, Vancouver, British Columbia, CanadaAdversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in their previous work [21]. In addition, we develop new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we provide an alternative proof of the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting.https://www.cambridge.org/core/product/identifier/S0956792524000822/type/journal_articleexistence of solutions for minimax problemsnonparametric robustnessgeneral topics in artificial intelligenceproblem-solving in the context of artificial intelligence49J3562G3568T20 |
| spellingShingle | Nicolás García Trillos Matt Jacobs Jakwang Kim On the existence of solutions to adversarial training in multiclass classification European Journal of Applied Mathematics existence of solutions for minimax problems nonparametric robustness general topics in artificial intelligence problem-solving in the context of artificial intelligence 49J35 62G35 68T20 |
| title | On the existence of solutions to adversarial training in multiclass classification |
| title_full | On the existence of solutions to adversarial training in multiclass classification |
| title_fullStr | On the existence of solutions to adversarial training in multiclass classification |
| title_full_unstemmed | On the existence of solutions to adversarial training in multiclass classification |
| title_short | On the existence of solutions to adversarial training in multiclass classification |
| title_sort | on the existence of solutions to adversarial training in multiclass classification |
| topic | existence of solutions for minimax problems nonparametric robustness general topics in artificial intelligence problem-solving in the context of artificial intelligence 49J35 62G35 68T20 |
| url | https://www.cambridge.org/core/product/identifier/S0956792524000822/type/journal_article |
| work_keys_str_mv | AT nicolasgarciatrillos ontheexistenceofsolutionstoadversarialtraininginmulticlassclassification AT mattjacobs ontheexistenceofsolutionstoadversarialtraininginmulticlassclassification AT jakwangkim ontheexistenceofsolutionstoadversarialtraininginmulticlassclassification |