Research map / Optimization / Nonconvex and smooth optimization
Pairwise Conditional Gradients without Swap Steps and Sparser Kernel Herding
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace PCG swap steps with local pairwise steps plus blending with global FW steps (BPCG) | Pairwise Conditional Gradients · Probability simplex n=200 | computational time convergence | Helped |
| Use BPCG (blended pairwise steps) instead of vanilla pairwise steps | Frank-Wolfe style sparse optimization · Probability simplex n=500 | sparsity of iterates (number of atoms) | Helped |
| Use BPCG instead of Vanilla/Away/Pairwise CG | Birkhoff polytope quadratic problem · Birkhoff polytope n=200 | sparsity of solution | Helped |
| Use BPCG instead of Vanilla/Away/Pairwise CG | Birkhoff polytope quadratic problem · Birkhoff polytope n=200 | dual gap vs iterations/time | Mixed |
| Use BPCG for matrix completion over spectrahedron | Frank-Wolfe on spectrahedron · MovieLens matrix completion | sparsity of solution | Helped |
| Apply BPCG to kernel herding (sparse quadrature) | Kernel herding · Matérn kernel (nu=3/2) and (nu=5/2), d=2 | MMD vs number of nodes | Helped |
| Apply BPCG to kernel herding; laziness for computational time | Kernel herding · Matérn kernel (nu=3/2), d=2 | MMD vs computational time | Helped |
| Apply BPCG to kernel herding instead of plain kernel herding in terms of iterations | Kernel herding · Matérn kernel (nu=3/2), d=2 | MMD vs number of iterations | No clear effect |
| Apply BPCG to kernel herding | Kernel herding · Gaussian kernel d=2 | MMD vs number of nodes | Helped |
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