Research map / Optimization / Nonconvex and smooth optimization
Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use nonsmooth convex losses rather than sufficiently smooth convex losses | GD and SGD · Nonsmooth convex losses | UAS: additional \eta\sqrt{T} term | Hurt |
| Use smaller constant step size and more iterations to control the additional stability term | Full-batch GD · Nonsmooth SCO | expected excess population risk: O(LR/\sqrt n) | Helped |
| Add Gaussian noise to SGD and run n^2 iterations | Noisy SGD · Nonsmooth DP-SCO | excess population risk: RL\cdot O\left(\max\left(\frac{\log(n)\log(n/\theta)}{\sqrt{n}}, ~\frac{\sqrt{d\,\log(1/\beta)}}{\alpha\, n}\right)\righ | Helped |
| Add the same noise sequence to both neighboring-data trajectories | Noisy SGD · Nonsmooth DP-SCO | UAS | No clear effect |
| Use fixed-permutation SGD without reshuffling or other randomization | Fixed-permutation SGD · Nonsmooth SCO | high-probability excess population risk: \frac{cLR}{\sqrt n} \log n\log(\frac{n}{\theta}) | Helped |
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