Research map / Optimization / Nonconvex and smooth optimization
SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path-Integrated Differential Estimator
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SPIDER gradient tracking with normalized gradient descent | Non-convex online first-order optimization · Online non-convex optimization | stochastic gradient complexity: \varepsilon^{-3.333} -> \varepsilon^{-3} | Helped |
| Use SPIDER gradient tracking with normalized gradient descent | Non-convex finite-sum first-order optimization · Finite-sum non-convex optimization | gradient cost: n + n^{2/3}\varepsilon^{-2} -> n + n^{1/2}\varepsilon^{-2} | Helped |
| Split negative-curvature descent into small steps while maintaining the SPIDER gradient estimate | SPIDER-SFO+ · Online non-convex optimization, second-order stationary point | gradient cost: \varepsilon^{-3.5} -> \varepsilon^{-3} | Helped |
| Split negative-curvature descent into small steps while maintaining the SPIDER gradient estimate | SPIDER-SFO+ · Finite-sum non-convex optimization, n\geq\Omega(\varepsilon^{-1}) | gradient cost: n \varepsilon^{-1.5} + n^{3/4} \varepsilon^{-1.75} -> n^{1/2} \epsilon^{-2} | Helped |
| Apply SPIDER variance reduction to zeroth-order gradient estimates | SPIDER-SZO · Stochastic zeroth-order optimization | individual function accesses: \mathcal{O}(d\epsilon^{-4}) -> \mathcal{O}( d\min(n^{1/2}\epsilon^{-2}, d\epsilon^{-3})) | Helped |
| Use SPIDER-SFO+ without the acceleration techniques discussed for small n | Finite-sum second-order optimization · Finite-sum non-convex optimization, n=\mathcal{O}(\epsilon^{-1}) | gradient cost: \tilde{\mathcal{O}}(n^{3/4} \varepsilon^{-1.75}) -> \tilde{\mathcal{O}}(\varepsilon^{-2.5}) | Hurt |
Closest papers by meaning
- Conditional Gradient Methods via Stochastic Path-Integrated Differential Estimator (ICML 2019 · similarity 0.91)
- D-SPIDER-SFO: A Decentralized Optimization Algorithm with Faster Convergence Rate for Nonconvex Problems (AAAI 2020 · similarity 0.90)
- Universal Gradient Methods for Stochastic Convex Optimization (ICML 2024 · similarity 0.88)
- High-Probability Bound for Non-Smooth Non-Convex Stochastic Optimization with Heavy Tails (ICML 2024 · similarity 0.88)
- Second-Order Convergence in Private Stochastic Non-Convex Optimization (NeurIPS 2025 · similarity 0.87)
- Universality of AdaGrad Stepsizes for Stochastic Optimization: Inexact Oracle, Acceleration and Variance Reduction (NeurIPS 2024 · similarity 0.87)
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