Research map / Optimization / Nonconvex and smooth optimization
Uniform-in-Time Wasserstein Stability Bounds for (Noisy) Stochastic Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Markov-chain perturbation bounds with contraction, a Lyapunov drift condition, and a bound on transition-kernel perturbation | SGD on quadratic losses · Quadratic losses | 1-Wasserstein stability: the bound is proportional to 1/n | Helped |
| Use strongly convex losses and the stated pseudo-Lipschitz-like gradient condition | SGD · Strongly convex losses | 1-Wasserstein stability: the bound is proportional to 1/n | Helped |
| Add independent full-support noise with finite second moment | SGD on dissipative non-convex losses · Dissipative non-convex losses | 1-Wasserstein stability: the bound has a factor 2b/n | Helped |
| Remove the additional additive noise (ablation) | Noisy SGD on dissipative non-convex losses · Dissipative non-convex losses | generalization-bound rate: n^{-1} -> n^{-1/2} | Hurt |
| Remove the additional additive noise (ablation) | SGD on dissipative non-convex losses · Dissipative non-convex losses | 2-Wasserstein stability squared: the bound includes 2K/m | Hurt |
| Relax strong convexity to the stated p-growth condition, with p in (1,2) (ablation) | SGD in the stationary regime · Convex losses with additional geometric structure | generalization-bound rate: n^{-1} -> n^{-1/p} | Hurt |
| Use noisy SGD with non-Gaussian noise rather than requiring Gaussian noise | SGD on dissipative non-convex losses · Dissipative non-convex losses | time-uniform stability | Helped |
| Use a Lipschitz surrogate loss to measure stability | Wasserstein stability analysis of SGD · All considered loss classes | generalization bound applicability | Hurt |
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