Research map / Optimization / Nonconvex and smooth optimization
Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace random perturbation or random search with zeroth-order negative-curvature finding | Deterministic ZO local-minimum finding · SOSP finding | function queries: \mathcal{O}\left( \frac{d}{\epsilon^2} + \frac{d \log d}{\delta^{3.5}} \right) | Helped |
| Add zeroth-order NCF to stochastic ZO methods instead of using cubic regularization | Stochastic ZO local-minimum finding · SOSP finding | function queries: \tilde{\mathcal{O}}\left( \frac{d}{\epsilon^{3}} + \frac{d}{\epsilon^2 \delta^2} + \frac{d}{\delta^5} \right) | Helped |
| Use random search rather than gradient-based updates | RSPI · Octopus function, growing dimensions | function value | Hurt |
| Use coordinate-wise instead of random-direction gradient estimation | ZO-GD-NCF · Deterministic SOSP finding | function queries: \tilde{\mathcal{O}} ( \frac{d^2\ell \Delta_f}{\epsilon^2} + d \frac{\sqrt{\ell}}{\sqrt{\delta}} \frac{\rho^2 \Delta_f}{\ | Helped |
| Use coordinate-wise instead of random-direction gradient estimation | ZO-SGD-NCF · Stochastic SOSP finding | function queries: \tilde{\mathcal{O}} (\frac{d^2 \sigma^2 \ell \Delta_f}{\epsilon^4} + \frac{d \sigma^2 \rho^2 \Delta_f}{\epsilon^2 \delta | Helped |
| Split the negative-curvature move into equal-length mini-steps | ZO-SPIDER-NCF · Stochastic SOSP finding | function queries: by a fact of \delta | Helped |
Closest papers by meaning
- First-order Stochastic Algorithms for Escaping From Saddle Points in Almost Linear Time (NeurIPS 2018 · similarity 0.90)
- Escape saddle points by a simple gradient-descent based algorithm (NeurIPS 2021 · similarity 0.89)
- Riemannian Accelerated Zeroth-order Algorithm: Improved Robustness and Lower Query Complexity (ICML 2024 · similarity 0.86)
- Second-Order Min-Max Optimization with Lazy Hessians (ICLR 2025 · similarity 0.84)
- Efficiently Escaping Saddle Points under Generalized Smoothness via Self-Bounding Regularity (NeurIPS 2025 · similarity 0.83)
- The Computational Complexity of Finding Second-Order Stationary Points (ICML 2024 · similarity 0.83)
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