Simplifying Adversarially Robust PAC Learning with Tolerance
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913686060269568 |
|---|---|
| author | Ashtiani, Hassan Pathak, Vinayak Urner, Ruth |
| author_facet | Ashtiani, Hassan Pathak, Vinayak Urner, Ruth |
| contents | Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential in the VC-dimension. A series of follow up work considered a slightly relaxed version of the problem called adversarially robust learning with tolerance [Ashtiani et al., 2023, Bhattacharjee et al., 2023, Raman et al., 2024] and achieved better sample complexity in terms of the VC-dimension. However, those algorithms were either improper and complex, or required additional assumptions on the hypothesis class H. We prove, for the first time, the existence of a simpler learner that achieves a sample complexity linear in the VC-dimension without requiring additional assumptions on H. Even though our learner is improper, it is "almost proper" in the sense that it outputs a hypothesis that is "similar" to a hypothesis in H.
We also use the ideas from our algorithm to construct a semi-supervised learner in the tolerant setting. This simple algorithm achieves comparable bounds to the previous (non-tolerant) semi-supervised algorithm of Attias et al. [2022a], but avoids the use of intricate subroutines from previous works, and is "almost proper." |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplifying Adversarially Robust PAC Learning with Tolerance Ashtiani, Hassan Pathak, Vinayak Urner, Ruth Machine Learning Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential in the VC-dimension. A series of follow up work considered a slightly relaxed version of the problem called adversarially robust learning with tolerance [Ashtiani et al., 2023, Bhattacharjee et al., 2023, Raman et al., 2024] and achieved better sample complexity in terms of the VC-dimension. However, those algorithms were either improper and complex, or required additional assumptions on the hypothesis class H. We prove, for the first time, the existence of a simpler learner that achieves a sample complexity linear in the VC-dimension without requiring additional assumptions on H. Even though our learner is improper, it is "almost proper" in the sense that it outputs a hypothesis that is "similar" to a hypothesis in H. We also use the ideas from our algorithm to construct a semi-supervised learner in the tolerant setting. This simple algorithm achieves comparable bounds to the previous (non-tolerant) semi-supervised algorithm of Attias et al. [2022a], but avoids the use of intricate subroutines from previous works, and is "almost proper." |
| title | Simplifying Adversarially Robust PAC Learning with Tolerance |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.07232 |