Name
Abstract | ||
|---|---|---|
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization.In this paper, we apply the momentum scheme to cubic regularized (CR) Newtonu0027s method and explore the potential for acceleration. Our numerical experiments on various nonconvex optimization problems demonstrate that the momentum scheme can substantially facilitate the convergence of cubic regularization, and perform even better than the Nesterovu0027s acceleration scheme for CR. Theoretically, we prove that CR under momentum achieves the best possible convergence rate to a second-order stationary point for nonconvex optimization. Moreover, we study the proposed algorithm for solving problems satisfying an error bound condition and establish a local quadratic convergence rate. Then, particularly for finite-sum problems, we show that the proposed algorithm can allow computational inexactness that reduces the overall sample complexity without degrading the convergence rate. |
Year | Venue | Field |
|---|---|---|
2018 | UAI | Convergence (routing),Mathematical optimization,Stationary point,Regularization (mathematics),Rate of convergence,Momentum,Acceleration,Sample complexity,Optimization problem,Mathematics |
DocType | Volume | Citations |
Journal | abs/1810.03763 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wang, Zhe | 1 | 4 | 4.13 |
| Yi Zhou | 2 | 65 | 17.55 |
| Yingbin Liang | 3 | 1646 | 147.64 |
| Guanghui Lan | 4 | 1212 | 66.26 |