Research map / Optimization / Nonconvex and smooth optimization
Variance-Reduced and Projection-Free Stochastic Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add variance reduction to SFW, yielding SVRF | SFW · Smooth convex optimization | # stochastic gradients: \mathcal{O}(\frac{1}{\epsilon^3}) -> \mathcal{O}(\frac{1}{\epsilon^2}) | Helped |
| Add variance reduction to SCGS, yielding STORC | SCGS · Smooth, G-Lipschitz optimization | # stochastic gradients: \mathcal{O}(\frac{1}{\epsilon^2}) -> \mathcal{O}(\frac{1}{\epsilon^{1.5}}) | Helped |
| Add variance reduction to SCGS, yielding STORC | SCGS · Smooth, strongly convex optimization | # stochastic gradients: \mathcal{O}(\frac{1}{\epsilon}) -> \mathcal{O}(\mu^2 \ln \frac{LD^2}{\epsilon}) | Helped |
| Add variance reduction to SCGS, yielding STORC | SCGS · Optimization with ∇f(w*) = 0 | # stochastic gradients: \mathcal{O}(\frac{1}{\epsilon^2}) -> \mathcal{O}(\frac{1}{\epsilon}) | Helped |
| Use variance reduction in place of ordinary stochastic gradients | Projection-free methods on multiclass classification · news20, rcv1, aloi | loss versus running time | Helped |
| Use projection-free methods instead of projected SGD or SVRG | Multiclass classification · news20, rcv1, aloi | loss versus running time | Helped |
| Use STORC instead of the simpler SFW or SVRF | Projection-free multiclass classification · news20, rcv1, aloi | loss versus running time | Hurt |
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