Name
Abstract | ||
|---|---|---|
We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation of mirror descent with a recent ODE interpretation of Nesterov's accelerated method, we propose a family of continuous-time descent dynamics for convex functions with Lipschitz gradients, such that the solution trajectories converge to the optimum at a O(1/t2) rate. We then show that a large family of first-order accelerated methods can be obtained as a discretization of the ODE, and these methods converge at a O(1/k2) rate. This connection between accelerated mirror descent and the ODE provides an intuitive approach to the design and analysis of accelerated first-order algorithms. |
Year | Venue | Field |
|---|---|---|
2015 | Annual Conference on Neural Information Processing Systems | Discretization,Mathematical optimization,Descent direction,Convex function,Lipschitz continuity,Discrete time and continuous time,Ode,Mathematics |
DocType | Volume | ISSN |
Conference | 28 | 1049-5258 |
Citations | PageRank | References |
22 | 1.11 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Walid Krichene | 1 | 108 | 14.02 |
| A. M. Bayen | 2 | 27 | 2.69 |
| Peter L. Bartlett | 3 | 5482 | 1039.97 |