Research map / Optimization / Nonconvex and smooth optimization
SDCA without Duality, Regularization, and Individual Convexity
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Dual-free SDCA (Algorithm 1) with non-uniform sampling q_i=(L_i+Lbar)/(2n Lbar) on regularized convex objectives | Dual-free SDCA · regularized convex loss minimization | iteration complexity T | Helped |
| Remove explicit regularization by adding artificial regularization and a concave compensating function (Algorithm 2) | Dual-free SDCA for non-regularized objectives · unregularized convex objectives | iteration complexity T | No clear effect |
| Use non-convex individual losses (SDCA with lambda-strongly convex expected loss) instead of convex losses | Dual-free SDCA non-convex case · non-convex individual losses | iteration complexity T: T ~ Lbar^2/lambda^2 + n vs Lbar/lambda + n for convex | Hurt |
| Add Catalyst-style acceleration to dual-free SDCA for non-convex individual losses | Dual-free SDCA non-convex case · non-convex individual losses | iteration complexity T: from n + Lbar^2/lambda^2 to n + n^{3/4} sqrt(Lbar/lambda) | Helped |
| Acceleration applied to convex-case SDCA | Dual-free SDCA convex case · convex individual losses | iteration complexity: from Lbar/lambda to n^{1/2} sqrt(Lbar/lambda)+n | Helped |
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