Agnostic Multi-Robust Learning Using ERM

• URL: http://arxiv.org/abs/2303.08944v2
• Date: Tue, 13 Feb 2024 03:24:23 GMT
• Title: Agnostic Multi-Robust Learning Using ERM
• Authors: Saba Ahmadi, Avrim Blum, Omar Montasser, Kevin Stangl
• Abstract summary: A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test-time natural example. In contrast, the attacker only needs to find one successful perturbation. We introduce a novel multi-group setting and introduce a novel multi-robust learning problem.
• Score: 19.313739782029185
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test-time natural example. In contrast, the attacker only needs to find one successful perturbation. Xiang et al.[2022] proposed an algorithm that in the context of patch attacks for image classification, reduces the effective number of perturbations from an exponential to a polynomial number of perturbations and learns using an ERM oracle. However, to achieve its guarantee, their algorithm requires the natural examples to be robustly realizable. This prompts the natural question; can we extend their approach to the non-robustly-realizable case where there is no classifier with zero robust error? Our first contribution is to answer this question affirmatively by reducing this problem to a setting in which an algorithm proposed by Feige et al.[2015] can be applied, and in the process extend their guarantees. Next, we extend our results to a multi-group setting and introduce a novel agnostic multi-robust learning problem where the goal is to learn a predictor that achieves low robust loss on a (potentially) rich collection of subgroups.

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