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We analyze a class of exact distributed first order methods under a generalsetting on the underlying network and step-sizes. In more detail, we allowsimultaneously for time-varying uncoordinated stepsizes and time-varyingdirected weight-balanced networks, jointly connected over bounded intervals.The analyzed class of methods subsumes several existing algorithms like theunified Extra and unified DIGing (Jakovetic, 2019), or the exact spectralgradient method (Jakovetic, Krejic, Krklec Jerinkic, 2019) that have beenanalyzed before under more restrictive assumptions. Under the assumed setting,we establish R-linear convergence of the methods and present severalimplications that our results have on the literature. Most notably, we showthat the unification strategy in (Jakovetic, 2019) and the spectral step-sizeselection strategy in (Jakovetic, Krejic, Krklec Jerinkic, 2019) exhibit a highdegree of robustness to uncoordinated time-varying step sizes and totime-varying networks.

Linear Convergence Rate Analysis of a Class of Exact First-Order  Distributed Methods for Weight-Balanced Time-Varying Networks and  Uncoordinated Step Sizes