Efficiently Learning Adversarially Robust Halfspaces with Noise

Abstract

We study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces are efficiently robustly learnable. In the presence of random label noise, we give a simple computationally efficient algorithm for this problem with respect to any ${\ell }_p$-perturbation.

References in corpus (6)

• Exploring the Landscape of Spatial Robustness
• Testing Robustness Against Unforeseen Adversaries
• VC Classes are Adversarially Robustly Learnable, but Only Improperly
• Adversarial Risk Bounds via Function Transformation
• On Robustness to Adversarial Examples and Polynomial Optimization
• On the Hardness of Robust Classification

Cited by in corpus (6)

• The Curious Case of Adversarially Robust Models: More Data Can Help, Double Descend, or Hurt Generalization
• The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise
• Reducing Adversarially Robust Learning to Non-Robust PAC Learning
• Robust learning under clean-label attack
• Self-Training of Halfspaces with Generalization Guarantees under Massart Mislabeling Noise Model
• Lower Bounds on Cross-Entropy Loss in the Presence of Test-time Adversaries