Research map / Optimization / Nonconvex and smooth optimization
Direct Runge-Kutta Discretization Achieves Acceleration
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an order-4 rather than order-1 Runge-Kutta integrator for direct discretization (ablation) | DD on the quadratic objective · Quadratic objective | stability and convergence rate: eventually unstable -> O(N^{-2}) | Helped |
| Use an order-1 integrator for direct discretization (ablation) | DD on the quadratic objective · Quadratic objective | stability: eventually unstable | Hurt |
| Use q greater than 2 when the objective satisfies the flatness condition with p=2 (ablation) | DD on the quadratic objective · Quadratic objective | stability: diverges | Hurt |
| Set q=6 for an objective satisfying the flatness condition with p=4 (ablation) | DD on the ℓ4 objective · ℓ4 objective | convergence rate: roughly O(N^{-5}) | Helped |
| Increase q (ablation) | DD on logistic loss · Logistic loss | objective decrease | Helped |
| Use DD instead of GD | Optimization of the quadratic plus quartic objective · Quadratic plus quartic objective | convergence rate | Helped |
| Use DD with q>2 instead of NAG | Optimization of the ℓ4 objective · ℓ4 objective | convergence rate | Helped |
| Use a larger q (ablation) | DD on logistic loss · Logistic loss | objective decrease | Helped |
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