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Adaptive gradient-based optimization methods such as \textsc{Adagrad},\textsc{Rmsprop}, and \textsc{Adam} are widely used in solving large-scalemachine learning problems including deep learning. A number of schemes havebeen proposed in the literature aiming at parallelizing them, based oncommunications of peripheral nodes with a central node, but incur highcommunications cost. To address this issue, we develop a novel consensus-baseddistributed adaptive moment estimation method (\textsc{Dadam}) for onlineoptimization over a decentralized network that enables data parallelization, aswell as decentralized computation. The method is particularly useful, since itcan accommodate settings where access to local data is allowed. Further, asestablished theoretically in this work, it can outperform centralized adaptivealgorithms, for certain classes of loss functions used in applications. Weanalyze the convergence properties of the proposed algorithm and provide adynamic regret bound on the convergence rate of adaptive moment estimationmethods in both stochastic and deterministic settings. Empirical resultsdemonstrate that \textsc{Dadam} works also well in practice and comparesfavorably to competing online optimization methods.

DADAM: A Consensus-based Distributed Adaptive Gradient Method for Online Optimization