Linear convergence of cyclic SAGA

• DOI: 10.1007/s11590-019-01520-y
• Publication Date: 2020-01-04T11:03:04Z
• Authors: Youngsuk Park; Ernest K. Ryu
• Keywords: Optimization and Control (math.OC); 0211 other engineering and technologies; FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; 02 engineering and technology; Mathematics - Optimization and Control

Published in Optimization Letters<br/>In this work, we present and analyze C-SAGA, a (deterministic) cyclic variant of SAGA. C-SAGA is an incremental gradient method that minimizes a sum of differentiable convex functions by cyclically accessing their gradients. Even though the theory of stochastic algorithms is more mature than that of cyclic counterparts in general, practitioners often prefer cyclic algorithms. We prove C-SAGA converges linearly under the standard assumptions. Then, we compare the rate of convergence with the full gradient method, (stochastic) SAGA, and incremental aggregated gradient (IAG), theoretically and experimentally.<br/>