Research map / Optimization / Nonconvex and smooth optimization
Escaping Saddle-Point Faster under Interpolation-like Conditions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply SGC to PSGD in the higher-order setting | PSGD · Nonconvex stochastic optimization, higher-order oracle | oracle calls to reach an ε-local minimizer: \torder\left({\epsilon}^{-4}\right) -> \tilde{\mathcal{O}}\left(\frac{\log\left(\frac{1}{\delta}\right)}{{\epsilon}^2}\r | Helped |
| Apply SGC to PSGD with zeroth-order estimates | PSGD · Nonconvex stochastic optimization, zeroth-order oracle | oracle calls to reach an ε-local minimizer: \tilde{\mathcal{O}}\left(\frac{d^{1.5}\sigma}{{\epsilon}^{5.5}}\right) -> \tilde{\mathcal{O}}\left(\frac{d^{1.5}\sqrt{\r | Helped |
| Apply SGC to SCRN in the higher-order setting | SCRN · Nonconvex stochastic optimization, higher-order oracle | oracle calls to reach an ε-local minimizer: \torder\left({\epsilon}^{-3.5}\right) -> \order\left({\epsilon^{-\frac{5}{2}}}\right) | Helped |
| Use gradient-level SGC for SCRN rather than a Hessian-level interpolation assumption | SCRN · Nonconvex stochastic optimization, higher-order oracle | oracle calls to reach an ε-local minimizer: \order\left({\epsilon^{-\frac{5}{2}}}\right) vs. \order\left({\epsilon^{-1.5}}\right) | Mixed |
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