Research map / Optimization / Nonconvex and smooth optimization
Beyond Lipschitz: Sharp Generalization and Excess Risk Bounds for Full-Batch GD
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use full-batch GD instead of SGD for smooth convex losses with limited model capacity | Full-batch GD · Smooth convex losses, limited model capacity | iterations to achieve excess risk 𝒪(1/√n): T=√n versus T=n | Helped |
| Use full-batch GD instead of SGD for smooth convex losses with limited model capacity | Full-batch GD · Smooth convex losses, limited model capacity | excess risk: 𝒪(1/√n) versus 𝒪(1/√n) | No clear effect |
| Use full-batch GD instead of SGD for smooth strongly convex objectives | Full-batch GD · Smooth strongly convex objective | iterations for the stated excess-risk rate: T=Θ(log n) versus T=Θ(n) | Helped |
| Use full-batch GD instead of SGD for smooth strongly convex objectives | Full-batch GD · Smooth strongly convex objective | excess risk: 𝒪(√(log(n))/n) versus 𝒪(1/n) | Mixed |
| Use full-batch GD rather than SGD on smooth convex non-Lipschitz losses | Full-batch GD · Smooth convex losses | generalization error: 𝒪(T/n) versus 𝒪(√(T/n)) | Helped |
| Train full-batch GD for T=√n rather than T=n in the convex limited-capacity setting | Full-batch GD · Smooth convex losses, limited model capacity | excess risk: 𝒪(1/√n) at T=√n; 𝒪(1/√n) at T=n | No clear effect |
| Train full-batch GD for T=n under interpolation rather than stop at T=√n | Full-batch GD · Smooth convex losses, interpolation | excess risk: 𝒪(1/√n) to 𝒪(1/n) | Helped |
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