Research map / Optimization / Implicit bias and generalization
Agnostic Learning of Halfspaces with Gradient Descent via Soft Margins
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply convex gradient descent when the optimal halfspace has a hard margin | Halfspace agnostic learning · Hard margin distributions | classification error: \tilde O(\bar \gamma^{-1} \mathsf{OPT}) + \varepsilon | Helped |
| Apply convex gradient descent when projections satisfy anti-concentration | Halfspace agnostic learning · Sub-exponential distributions with anti-concentration | classification error: \tilde O(\mathsf{OPT}^{1/2}) + \varepsilon | Helped |
| Use an exponential-tail rather than polynomial-tail loss | Gradient descent on linearly separable data · Linearly separable data | sample complexity: \Omega(\gamma^{-2} \varepsilon^{-2-2/p}) versus \tilde \Omega(\gamma^{-2} \varepsilon^{-2}) | Helped |
| Use online stochastic gradient descent instead of full-batch gradient descent | Surrogate-risk minimization on bounded distributions · Bounded distributions | sample complexity rate: O(\varepsilon^{-2}) to O(\varepsilon^{-1}) | Helped |
| Use the soft-margin conversion with uniform-sphere marginals | Soft-margin analysis for halfspace learning · Uniform distribution on the unit sphere | dimension dependence of the soft margin: \Omega(\gamma \sqrt d) | Hurt |
Closest papers by meaning
- A Near-optimal Algorithm for Learning Margin Halfspaces with Massart Noise (NeurIPS 2024 · similarity 0.89)
- Reliable Learning of Halfspaces under Gaussian Marginals (NeurIPS 2024 · similarity 0.88)
- Learning Noisy Halfspaces with a Margin: Massart is No Harder than Random (NeurIPS 2024 · similarity 0.88)
- An Efficient Tester-Learner for Halfspaces (ICLR 2024 · similarity 0.87)
- Smoothed Agnostic Learning of Halfspaces over the Hypercube (NeurIPS 2025 · similarity 0.87)
- Replicable Learning of Large-Margin Halfspaces (ICML 2024 · similarity 0.86)
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