Research map / Optimization / Nonconvex and smooth optimization
Stochastic Bias-Reduced Gradient Methods
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply multilevel Monte Carlo debiasing to an optimal-distance-convergence method | Stochastic estimation of strongly-convex minimizers · Strongly-convex stochastic optimization | expected stochastic gradient evaluations: O(\log T) stochastic gradient evaluations; T iterations of SGD | Helped |
| Use bias-reduced Moreau-envelope gradient estimates | Stochastic accelerated gradient descent · Projection-efficient convex optimization | stochastic gradient evaluations: O( (GD/ε)^3 ) -> O\left(\frac{G^2 D^2}{\epsilon^2} \log^2 \left( \frac{G R}{\epsilon} \right) \right) | Helped |
| Use bias-reduced Moreau-envelope gradient estimates and an improved choice of minimum regularization | Accelerated proximal point method · Minimizing maximum of N convex functions | function evaluation complexity: \Otil{ N\epsilon^{-2/3} + \epsilon^{-8/3} } -> O\left( \left[ N \left( \frac{GR\log N}{\epsilon}\right)^{2/3} + \left(\f | Helped |
| Estimate composite proximal points with the low-bias optimum estimator | Composite accelerated gradient descent · Gradient-efficient composite optimization | stochastic gradient evaluations: O((GR/ε)^2) -> O\left(\prn*{\frac{GR}{\epsilon}}^2\log^2\frac{GR}{\epsilon}+ \sqrt{\frac{LR^2}{\epsilon}}\log\left(\frac | Mixed |
| Assume an efficient bounded low-bias optimum estimator | Localization-based private stochastic convex optimization · Non-smooth differentially private stochastic convex optimization | subgradient evaluations: O(n^{11/8}) -> \Otil{n} | Helped |
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