Research map / Learning theory and algorithms / Matrix and tensor methods
Online Partial Least Square Optimization: Dropping Convexity for Better Efficiency and Scalability
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace convex MSG (lifted nuclear-norm relaxation with Fantope projection) with nonconvex projected SGD on the unit sphere (PSG) | Online PLS (rank-1) on MNIST subset (labels 3,4,5,9) · MNIST subset, n=23343, m=d=392 | iterations and wall-clock time to reach accuracy (log of 1 - (1/sqrt2)(u_k^T u_h | Helped |
| Replace convex MSG with nonconvex projected SGD (no expensive Fantope projection per iteration) | Online PLS wall-clock efficiency · MNIST subset, n=23343 | wall clock time | Helped |
| Use diminishing step size eta_k ~ k^-1 (lambda1-lambda2)^-1 log d instead of fixed step size | Nonconvex SGD for online PLS · synthetic and MNIST (empirical observation) | empirical convergence performance | Helped |
| Theoretical iteration complexity of nonconvex SGD vs convex MSG (O(eps^-2 log(1/eps))) | Online PLS · theory | iterations to eps-optimal: O(eps^-1 log(1/eps)) vs O(eps^-2 log(1/eps)), a factor of eps^-1 | Helped |
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