Optimal Distributed Optimization on Slowly Time-Varying Graphs [article]

Alexander Rogozin, César A. Uribe, Alexander Gasnikov, Nikolay Malkovsky, Angelia Nedić
2019 arXiv   pre-print
We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up lo logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We
more » ... call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Ω( (√(κ_Φ·χ̅) + αlog(κ_Φ·χ̅)) log(1 / ε)) for decentralized algorithms, where κ_Φ is condition number of the objective function, and χ̅ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.
arXiv:1805.06045v6 fatcat:4pgeocp6h5ehzbj3ygdkkmduhi