On the hardness of robust classification
It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory, considering both sample and computational complexity. In particula...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Neural Information Processing Systems Foundation
2019
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| _version_ | 1797059217232756736 |
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| author | Gourdeau, P Kanade, V Kwiatkowska, M Worrell, J |
| author_facet | Gourdeau, P Kanade, V Kwiatkowska, M Worrell, J |
| author_sort | Gourdeau, P |
| collection | OXFORD |
| description | It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory, considering both sample and computational complexity. In particular, our definition of robust learnability requires polynomial sample complexity. We start with two negative results. We show that no non-trivial concept class can be robustly learned in the distribution-free setting against an adversary who can perturb just a single input bit. We show moreover that the class of monotone conjunctions cannot be robustly learned under the uniform distribution against an adversary who can perturb input bits. However if the adversary is restricted to perturbing bits, then the class of monotone conjunctions can be robustly learned with respect to a general class of distributions (that includes the uniform distribution). Finally, we provide a simple proof of the computational hardness of robust learning on the boolean hypercube. Unlike previous results of this nature, our result does not rely on another computational model (e.g. the statistical query model) nor on any hardness assumption other than the existence of a hard learning problem in the PAC framework. |
| first_indexed | 2024-03-06T20:01:01Z |
| format | Conference item |
| id | oxford-uuid:274bdf38-35f5-41f4-9c53-76527d74f19a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:01:01Z |
| publishDate | 2019 |
| publisher | Neural Information Processing Systems Foundation |
| record_format | dspace |
| spelling | oxford-uuid:274bdf38-35f5-41f4-9c53-76527d74f19a2022-03-26T12:06:06ZOn the hardness of robust classificationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:274bdf38-35f5-41f4-9c53-76527d74f19aEnglishSymplectic Elements at OxfordNeural Information Processing Systems Foundation2019Gourdeau, PKanade, VKwiatkowska, MWorrell, JIt is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory, considering both sample and computational complexity. In particular, our definition of robust learnability requires polynomial sample complexity. We start with two negative results. We show that no non-trivial concept class can be robustly learned in the distribution-free setting against an adversary who can perturb just a single input bit. We show moreover that the class of monotone conjunctions cannot be robustly learned under the uniform distribution against an adversary who can perturb input bits. However if the adversary is restricted to perturbing bits, then the class of monotone conjunctions can be robustly learned with respect to a general class of distributions (that includes the uniform distribution). Finally, we provide a simple proof of the computational hardness of robust learning on the boolean hypercube. Unlike previous results of this nature, our result does not rely on another computational model (e.g. the statistical query model) nor on any hardness assumption other than the existence of a hard learning problem in the PAC framework. |
| spellingShingle | Gourdeau, P Kanade, V Kwiatkowska, M Worrell, J On the hardness of robust classification |
| title | On the hardness of robust classification |
| title_full | On the hardness of robust classification |
| title_fullStr | On the hardness of robust classification |
| title_full_unstemmed | On the hardness of robust classification |
| title_short | On the hardness of robust classification |
| title_sort | on the hardness of robust classification |
| work_keys_str_mv | AT gourdeaup onthehardnessofrobustclassification AT kanadev onthehardnessofrobustclassification AT kwiatkowskam onthehardnessofrobustclassification AT worrellj onthehardnessofrobustclassification |