Research map / Optimization / Nonconvex and smooth optimization
Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use non-uniform sampling of outer stages instead of uniform sampling | SSDC · General DC objective | stationarity measure: \frac{2\gamma\Delta}{K} + \frac{2\gamma c(1+\log (K))}{K} -> \frac{2\gamma(\Delta+c)(\alpha+1)}{K} | Helped |
| Solve each stage to accuracy c/k rather than epsilon | SSDC · General DC objective | stagewise computation | Helped |
| Use increasing regularization parameters when nu is known | SSDC-SPG · General DC objective with Holder-continuous gradient | iteration complexity: O(1/epsilon^{4/nu}) -> O(1/epsilon^{(1+3nu)/nu}) | Helped |
| Use increasing regularization parameters when nu is known | SSDC-SVRG · Finite-sum DC objective with smooth g | gradient complexity: \widetilde O(n/epsilon^{2/nu}) -> \widetilde O(n/epsilon^{(1+nu)/nu}) | Helped |
| Use AdaGrad for the stagewise subproblems | SSDC-AdaGrad · General DC objective | iteration complexity: O(1/epsilon^4) | Mixed |
| Represent the non-convex regularizer with its Moreau-envelope DC decomposition | Moreau-envelope SSDC · Non-convex non-smooth regularized objective | convergence guarantee | Helped |
| Use SVRG instead of SPG for finite-sum problems | Moreau-envelope SSDC · Non-convex non-smooth regularizer; Lipschitz r | complexity: O(1/epsilon^8) -> \widetilde O(n/epsilon^4) | Helped |
| Use SVRG instead of SPG for finite-sum problems | Moreau-envelope SSDC · Non-convex non-smooth regularizer; lower-bounded finite-valued r | complexity: O(1/epsilon^{12}) -> \widetilde O(n/epsilon^6) | Helped |
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