Research map / Learning theory and algorithms / Matrix and tensor methods
Learning General Halfspaces with Adversarial Label Noise via Online Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the prior sophisticated polynomial-time general-halfspace learner with online projected gradient descent on a sequence of localized ramp surrogate losses | learning general halfspaces with adversarial label noise under Gaussian marginals · theoretical guarantee (Gaussian marginal, adversarial label noise) | 0-1 error guarantee (C·ε, C universal constant) | Helped |
| Use online gradient descent with T = O(log^4(1/ε)) iterations on localized ramp losses instead of the prior poly(d/ε) algorithm | general halfspace learner · sample complexity and runtime | sample complexity Õ(d/ε^2 log(1/δ)) and near-linear runtime in N | Helped |
| Estimate the threshold t from empirical label mean via t' = Φ^{-1}((1 - E[y])/2) instead of assuming it is known | online gradient descent learner · theoretical analysis (Claim 4.7 / C.9) | additional error introduced | No clear effect |
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