Research map / Optimization / Nonconvex and smooth optimization
Adaptive Newton Sketch: Linear-time Optimization with Quadratic Convergence and Effective Hessian Dimensionality
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Adapt sketch size to the effective Hessian dimension instead of using a fixed ambient-dimension sketch | Newton Sketch on strongly convex self-concordant composite optimization · Strongly convex self-concordant composite optimization | time complexity: $nd \log(d) \log(1/\delta)$ -> $nd \log(\overline{d}_\mu)^2 \log(d/\delta)$ | Helped |
| Use quadratic rather than linear convergence (ablation) | NS-effdim with SRHT · Strongly convex self-concordant composite optimization | iteration count: $\mathcal{O}(\log(1/\delta))$ -> $\mathcal{O}(\log\log(1/\delta))$ | Helped |
| Use quadratic rather than linear convergence (ablation) | Adaptive Newton Sketch with SRHT · Strongly convex self-concordant composite optimization | iteration count: $\mathcal{O}(\log(\overline{d}_\mu)\log(d/\delta))$ -> $\mathcal{O}(\log(\overline{d}_\mu)\log\log(d/\delta))$ | Helped |
| Adapt sketch size using progress checks and doubling rather than fixing it in advance | Newton Sketch on regularized logistic regression · Regularized logistic regression | relative error versus CPU-time | Helped |
| Use SJLT rather than RRS sketching | Adaptive Newton Sketch · Regularized logistic regression datasets | sketch dimension | Mixed |
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