| Paper ID | SPTM-3.2 |
| Paper Title |
A DECENTRALIZED VARIANCE-REDUCED METHOD FOR STOCHASTIC OPTIMIZATION OVER DIRECTED GRAPHS |
| Authors |
Muhammad Qureshi, Tufts University, United States; Ran Xin, Soummya Kar, Carnegie Mellon University, United States; Usman Khan, Tufts University, United States |
| Session | SPTM-3: Estimation, Detection and Learning over Networks 1 |
| Location | Gather.Town |
| Session Time: | Tuesday, 08 June, 14:00 - 14:45 |
| Presentation Time: | Tuesday, 08 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [OPT] Optimization Methods for Signal Processing |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
In this paper, we propose a decentralized first-order stochastic optimization method PushSAGA for finite-sum minimization over a strongly connected directed graph. This method features local variance reduction to remove the uncertainty caused by random sampling of the local gradients, global gradient tracking to address the distributed nature of the data, and push-sum consensus to handle the imbalance caused by the directed nature of the underlying graph. We show that, for a sufficiently small step-size, PushSAGA linearly converges to the optimal solution for smooth and strongly convex problems, making it the first linearly-convergent stochastic algorithm over arbitrary strongly-connected directed graphs. We illustrate the behavior and convergence properties of PushSAGA with the help of numerical experiments for strongly convex and nonconvex problems. |
