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We propose ADOM - an accelerated method for smooth and strongly convexdecentralized optimization over time-varying networks. ADOM uses a dual oracle,i.e., we assume access to the gradient of the Fenchel conjugate of theindividual loss functions. Up to a constant factor, which depends on thenetwork structure only, its communication complexity is the same as that ofaccelerated Nesterov gradient method (Nesterov, 2003). To the best of ourknowledge, only the algorithm of Rogozin et al. (2019) has a convergence ratewith similar properties. However, their algorithm converges under the veryrestrictive assumption that the number of network changes can not be greaterthan a tiny percentage of the number of iterations. This assumption is hard tosatisfy in practice, as the network topology changes usually can not becontrolled. In contrast, ADOM merely requires the network to stay connectedthroughout time.

ADOM: Accelerated Decentralized Optimization Method for Time-Varying Networks