Research map / Optimization / Nonconvex and smooth optimization
Escape saddle points by a simple gradient-descent based algorithm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace uniform perturbation in PGD with negative curvature finding (NC-finding) | perturbed gradient descent · quartic test function with saddle at origin | iterations to escape saddle: less than $1/3$ times | Helped |
| replace perturbation in PSGD with SNC-finding | perturbed stochastic gradient descent · cubic test function | iterations to escape saddle: $1/2$ times | Helped |
| replace PAGD with ANCGD | perturbed accelerated gradient descent · nonconvex test functions | iterations to escape saddle: less than $1/3$ times | Helped |
| replace NEON+ with ANCGD | NEON+ · nonconvex test functions | iterations to escape saddle: $1/2$ times | Helped |
| use gradient-based negative curvature finding with single loop instead of nested-loop or higher log-power single-loop methods | non-stochastic saddle escaping · theory | iteration complexity: $\tilde{O}(\log^{6} n/\epsilon^{1.75})$ -> $\tilde{O}(\log n/\epsilon^{1.75})$ | Helped |
Closest papers by meaning
- Faster Gradient-Free Methods for Escaping Saddle Points (ICLR 2023 · similarity 0.95)
- Escaping Saddle Points in Constrained Optimization (NeurIPS 2018 · similarity 0.92)
- How to Escape Saddle Points Efficiently (ICML 2017 · similarity 0.92)
- Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioning (NeurIPS 2025 · similarity 0.87)
- Efficiently Escaping Saddle Points under Generalized Smoothness via Self-Bounding Regularity (NeurIPS 2025 · similarity 0.86)
- Second-Order Min-Max Optimization with Lazy Hessians (ICLR 2025 · similarity 0.85)
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