Research map / Learning theory and algorithms / Sample complexity
The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use L_∞ rather than a finite L_p norm, 2 ≤ p < ∞ | Proper ν-robust (1+δ)-agnostic halfspace learning · L_p-γ-margin halfspaces | runtime: (1/\delta)^{O\left(\frac{p}{\nu^2 \gamma^2}\right)} \cdot \poly(d/\epsilon) -> d^{O\left(\frac{\log(1/\delta)}{\nu^2 \ga | Hurt |
| Remove the margin gap by setting ν=0 | Proper robust agnostic learning of L_∞ halfspaces · L_∞-0.5-margin halfspaces | runtime feasibility: no \poly(d/\epsilon)-time learner | Hurt |
| Use the online-to-agnostic reduction with an online learner of mistake bound M | Proper agnostic learning of L_p-margin halfspaces · Empirical margin learning | runtime: \poly(|S|d) \cdot 2^{O(M\log(1/\delta))} | Helped |
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