On the convergence of decentralized gradient descent with diminishing stepsize, revisited
Woocheol Choi, Jimyeong Kim · arXiv (Cornell University) · 2022
Distributed optimization has received a lot of interest in recent years due to its wide applications in various fields. In this work, we revisit the convergence property of the decentralized gradient descent [A. Nedi{ć}-A.Ozdaglar (2009)] on the whole space given by $$ x_i(t+1) = \sum^m_{j=1}w_{ij}x_j(t) - α(t) abla f_i(x_i(t)), $$ where the stepsize is given as $α(t) = \frac{a}{(t+w)^p}$ with $00$ and $w>0$ are suitably chosen.