Research map / Optimization / Nonconvex and smooth optimization
Convergence of Stochastic Gradient Descent for PCA
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a streamed approximate power iteration to initialize SGD instead of uniform random initialization (ablation) | SGD (Oja's method) · Streaming PCA, no eigengap | normalized suboptimality: \mathcal{O}\left(\frac{\log(T)b\sqrt{d}}{\sqrt{T}}\right) -> \mathcal{O}\left(\frac{\log(T)b\sqrt{\log(d)n_A}}{\sqrt{T}} | Helped |
| Use a step size tuned to a positive eigengap and track suboptimality directly | SGD (Oja's method) · Streaming PCA, positive eigengap | normalized suboptimality: 1/\lambda^2 -> 1/\lambda | Helped |
| Use the eigengap-free step-size guarantee rather than requiring an eigengap | SGD (Oja's method) · Streaming PCA, no eigengap | normalized suboptimality | Helped |
Closest papers by meaning
- Stochastic PCA with $\ell_2$ and $\ell_1$ Regularization (ICML 2018 · similarity 0.92)
- Statistical Guarantees for High-Dimensional Stochastic Gradient Descent (NeurIPS 2025 · similarity 0.87)
- Oja's Algorithm for Streaming Sparse PCA (NeurIPS 2024 · similarity 0.87)
- Low Precision Streaming PCA (NeurIPS 2025 · similarity 0.87)
- Efficient Sparse PCA via Block-Diagonalization (ICLR 2025 · similarity 0.86)
- Demystifying SGD with Doubly Stochastic Gradients (ICML 2024 · similarity 0.86)
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