Research map / Optimization / Nonconvex and smooth optimization
Approximate Newton Methods and Their Local Convergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Sketch size set to several times d (ℓ=5d to 15d) instead of size scaling with condition number (ablation) | Sketch Newton · Least squares, A 10000x54 | linear convergence of log error | Helped |
| Lipschitz continuity of Hessian is not required (only needed for quadratic convergence) | Subsampled Newton variants · theory | convergence rate class | No clear effect |
| Adding regularizer αI to subsampled Hessian to allow smaller sample size (ablation) | Regularized subsampled Newton · Least squares, n=8000, d=5000 | convergence speed (iterations to precise solution): ~1200 iterations at |S|=600 vs ~8000 at |S|=100 | Helped |
| Too large regularizer α in regularized subsampled Newton (ablation) | Regularized subsampled Newton · Least squares, n=8000, d=5000 | convergence speed | Hurt |
| Small sample size without sufficiently large regularizer (ablation) | Regularized subsampled Newton · Least squares, n=8000, d=5000 | convergence (divergence) | Hurt |
| Small target rank r in NewSamp when sample size is small (ablation) | NewSamp · Least squares, n=8000, d=5000 | convergence (divergence) | Mixed |
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