Research map / Optimization / Nonconvex and smooth optimization
Tighter Analysis for ProxSkip
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace original Lyapunov function with inner-product variant (new analysis) | ProxSkip · proximal-operator-bottleneck regime (γ > γcrit) | decreasing speed of Lyapunov function: O(p^2) to O(p) | Helped |
| use a large step size instead of the algorithm-selected step size (ablation) | ProxSkip · Nesterov worst function, p=0.1 and p=0.01 | convergence rate: about twofold gap (p=0.1), around 20-fold gap (p=0.01) | Hurt |
| replace SProxSkip original analysis with new Lyapunov analysis | SProxSkip · stochastic gradient setting | proximal operator complexity: O(sqrt(1/(εµ^2)) log(1/ε)) to O(√κ log(1/ε)) | Helped |
| apply new Lyapunov function to ProxSkip-VR and GradSkip+ variants | ProxSkip-VR, GradSkip+ · theoretical convergence | decreasing speed of Lyapunov function | No clear effect |
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