ADOM: Accelerated Decentralized Optimization Method for Time-Varying Networks
This work addresses the challenge of efficient optimization in decentralized systems with unpredictable network topology changes, which is incremental but improves practical applicability over existing algorithms.
The authors tackled the problem of decentralized optimization over time-varying networks by proposing ADOM, an accelerated method that achieves a communication complexity similar to the accelerated Nesterov gradient method, up to a constant factor dependent on network structure, while only requiring the network to stay connected, unlike prior methods with restrictive assumptions on network changes.
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.