Research map / Optimization / Nonconvex and smooth optimization
Almost surely constrained convex optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Smoothing + homotopy on the constraint penalty (SASC) instead of projections onto matrix-valued constraints | stochastic gradient for almost-sure constrained problems · Basis pursuit, portfolio, SVM | convergence and practical performance | Helped |
| Tuning-free: no regularization parameter, step sizes from theory | SASC on hard margin SVM · kdd2010, rcv1, news20 test error | test error | No clear effect |
| Smoothing parameter mu of SPP set large (0.1) vs small (0.01) (ablation) | SPP on portfolio optimization · NYSE, DJIA, SP500, TSE distance to solution | distance to solution | Mixed |
| Mini-batch processing | SASC vs SPP · Basis pursuit mini-batches | computational overhead | Helped |
| Plain SGD on least squares objective instead of constrained formulation | SGD baseline · Synthetic basis pursuit | sparsity of recovered solution | Hurt |
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