Linear Convergence of Cyclic SAGA

TL;DR

This paper introduces C-SAGA, a cyclic variant of SAGA, and proves its linear convergence, providing theoretical and experimental comparisons with other gradient methods.

Contribution

The paper presents the first convergence analysis of C-SAGA, a cyclic incremental gradient method, demonstrating its linear convergence under standard assumptions.

Findings

C-SAGA converges linearly under standard assumptions.

C-SAGA's convergence rate is comparable to or better than other gradient methods.

Experimental results support the theoretical convergence claims.

Abstract

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.