Research map / Learning theory and algorithms / Sample complexity
On Proper Learnability between Average- and Worst-case Robustness
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the ρ-probabilistically robust threshold loss instead of a Lipschitz loss | Proper learning over VC classes with arbitrary adversaries · ρ-probabilistically robust PAC learning | proper learnability | Hurt |
| Use an L-Lipschitz loss on the expected perturbed margin | Finite-VC hypothesis classes · Lipschitz robust losses | proper learnability: O\left( \frac{\text{VC}({\mathcal{H}})L^2 \ln(\frac{L}{\epsilon}) + \ln(\frac{1}{\delta})}{\epsilon^2} \right) | Helped |
| Compete against the best hypothesis at a stricter probabilistic robustness level ρ* | PRERM · (ρ, ρ*)-probabilistically robust PAC learning | proper learnability: O\left(\frac{\frac{\text{VC}(\mathcal{H})}{(\rho-\rho^*)^2} \ln(\frac{1}{(\rho-\rho^*)\epsilon}) + \ln(\frac{1}{\delta}) | Helped |
| Use RERM while comparing against worst-case robust risk | Finite-VC hypothesis classes · (ρ, 𝒢)-probabilistically robust PAC learning | proper learnability: O\left( \frac{\frac{\text{VC}({\mathcal{H})}{\rho^2} \ln(\frac{1}{\rho \epsilon}) + \ln(\frac{1}{\delta})}{\epsilon^2} \ | Helped |
| Smooth an infinite-VC hypothesis class using a suitable perturbation measure | Lipschitz robust loss learning · Expected perturbed margin | proper learnability: O(\frac{L^2 + \ln(\frac{1}{\delta})}{\epsilon^2}) | Helped |
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