Variance-Reduced Decentralized Stochastic Optimization with Gradient Tracking -- Part II: GT-SVRG
This work addresses large-scale empirical risk minimization problems in decentralized settings, presenting an incremental improvement over existing methods.
The paper tackles decentralized stochastic optimization by developing GT-SVRG, a method combining gradient tracking with SVRG for variance reduction, showing it matches the convergence rate of GT-SAGA for smooth and strongly-convex functions and highlighting trade-offs between the two algorithms.
Decentralized stochastic optimization has recently benefited from gradient tracking methods \cite{DSGT_Pu,DSGT_Xin} providing efficient solutions for large-scale empirical risk minimization problems. In Part I \cite{GT_SAGA} of this work, we develop \textbf{\texttt{GT-SAGA}} that is based on a decentralized implementation of SAGA \cite{SAGA} using gradient tracking and discuss regimes of practical interest where \textbf{\texttt{GT-SAGA}} outperforms existing decentralized approaches in terms of the total number of local gradient computations. In this paper, we describe \textbf{\texttt{GT-SVRG}} that develops a decentralized gradient tracking based implementation of SVRG \cite{SVRG}, another well-known variance-reduction technique. We show that the convergence rate of \textbf{\texttt{GT-SVRG}} matches that of \textbf{\texttt{GT-SAGA}} for smooth and strongly-convex functions and highlight different trade-offs between the two algorithms in various settings.