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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. WearXiv:1805.06045v6 fatcat:4pgeocp6h5ehzbj3ygdkkmduhi