Research map / Optimization / Nonconvex and smooth optimization
Efficient Dictionary Learning with Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Negative curvature normal to stable manifolds of saddle points (vs. positive curvature in the same direction) | randomly initialized gradient descent on complete orthogonal dictionary learning · theoretical analysis (separable and dictionary learning objectives) | iterations to reach neighborhood of global minimum | Helped |
| Logarithmic dependence of iteration bound on the initialization-volume parameter zeta0 (vs. linear failure-probability dependence) | gradient descent convergence bound for separable objective · theoretical bound (Theorem 1) | iteration bound T and failure probability 1-P | Helped |
| Sample size p scaling for concentration of dictionary learning results | dictionary learning gradient descent analysis · theoretical analysis | required sample complexity p | No clear effect |
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