  We propose ADOM - an accelerated method for smooth and strongly convex
decentralized optimization over time-varying networks. ADOM uses a dual oracle,
i.e., we assume access to the gradient of the Fenchel conjugate of the
individual loss functions. Up to a constant factor, which depends on the
network structure only, its communication complexity is the same as that of
accelerated Nesterov gradient method (Nesterov, 2003). To the best of our
knowledge, only the algorithm of Rogozin et al. (2019) has a convergence rate
with similar properties. However, their algorithm converges under the very
restrictive assumption that the number of network changes can not be greater
than a tiny percentage of the number of iterations. This assumption is hard to
satisfy in practice, as the network topology changes usually can not be
controlled. In contrast, ADOM merely requires the network to stay connected
throughout time.
