Research map / Optimization / Nonconvex and smooth optimization
Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add acceleration to sketch-and-project | Sketch-and-project for linear systems · Linear systems in Euclidean spaces | iteration complexity: O((1/mu) log(1/epsilon)) -> O(sqrt(nu/mu) log(1/epsilon)) | Helped |
| Add acceleration with carefully chosen parameters | Stochastic matrix inversion · Artificial matrices and LIBSVM ridge-regression Hessians | convergence speed | Helped |
| Use coordinate sketches instead of Gaussian sketches (ablation) | Accelerated stochastic matrix inversion · LIBSVM ridge-regression Hessians | convergence speed | Mixed |
| Use estimated rather than exact acceleration parameters (ablation) | Accelerated stochastic matrix inversion · Artificial matrices and LIBSVM datasets | convergence speed | No clear effect |
| Set both mu and nu too small (ablation) | Accelerated stochastic matrix inversion · Sensitivity experiments on artificial matrices | convergence | Hurt |
| Enforce symmetry in the matrix-inversion iterates (ablation) | Accelerated stochastic matrix inversion · Positive definite matrix inversion | convergence rate: 2lambda_min(E[P]) >= lambda_min(E[Z]) >= lambda_min(E[P]) | Helped |
| Replace the standard deterministic BFGS update with the accelerated update | BFGS optimization · phishing, mushrooms, australian, splice | optimization convergence | Helped |
| Replace the standard deterministic BFGS update with the accelerated update (ablation) | BFGS optimization · madelon, covtype, a9a | optimization convergence | No clear effect |
| Use the accelerated deterministic BFGS update | BFGS optimization · phishing, mushrooms, australian, splice | time to convergence | Helped |
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