Research map / Optimization / Nonconvex and smooth optimization
Adaptive Gradient Methods for Constrained Convex Optimization and Variational Inequalities
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use per-coordinate adaptive step sizes in the accelerated constrained method | AdaACSA and AdaAGD+ · Constrained convex optimization, smooth | convergence rate: O\left(\frac{R_{\infty}^{2}\sum_{i=1}^{d}\beta_{i}\ln\beta_{i}}{T^{2}}+\frac{R_{\infty}\sqrt{d}\sigma\sqrt{\ln\left(\fra | Helped |
| Use acceleration rather than the non-accelerated AdaGrad+ scheme | AdaACSA and AdaAGD+ · Constrained convex optimization, smooth | convergence rate: O\left(\frac{R_{\infty}^{2}\sum_{i=1}^{d}\beta_{i}\ln\beta_{i}}{T^{2}}+\frac{R_{\infty}\sqrt{d}\sigma\sqrt{\ln\left(\fra | Helped |
| Adapt step sizes to the problem without prior knowledge of smoothness or gradient norms | AdaGrad+, AdaACSA, and AdaAGD+ · Constrained convex optimization, non-smooth | convergence rate: O\left(\frac{R_{\infty}\sqrt{d}G\sqrt{\ln\left(\frac{GT}{R_{\infty}}\right)}+R_{\infty}\sqrt{d}\sigma\sqrt{\ln\left(\fra | Helped |
| Set per-coordinate step sizes without an estimate of the operator norm | Adaptive Mirror Prox · Variational inequalities | duality gap convergence rate: O\left( \frac{R_{\infty}^{2}\sum_{i=1}^{d}\beta_{i}\ln\beta_{i}}{T} \right) | Helped |
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