Research map / Optimization / Nonconvex and smooth optimization
Third-order Smoothness Helps: Faster Stochastic Optimization Algorithms for Finding Local Minima
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use third-order smoothness to take a larger negative-curvature step | FLASH-Stochastic · General stochastic nonconvex optimization | stochastic gradient evaluations: eO(✏−7/2) -> eO(✏−10/3) | Helped |
| Use FLASH's larger negative-curvature step | Matrix sensing · Matrix sensing, d = 50 and d = 100 | objective function value versus oracle calls | Helped |
| Use FLASH's larger negative-curvature step | Deep autoencoder · MNIST autoencoders AE-1 and AE-2 | training and test loss versus oracle calls | Helped |
| Decrease the negative-curvature step size (ablation) | FLASH · Matrix sensing, d = 50 and d = 100 | objective function value versus oracle calls | Hurt |
| Use unperturbed first-order methods without negative-curvature escape | SGD, SGD-m, and SCSG · Matrix sensing | ability to escape saddle points | Hurt |
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