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We consider the problem of decentralized optimization where a collection ofagents, each having access to a local cost function, communicate over atime-varying directed network and aim to minimize the sum of those functions.In practice, the amount of information that can be exchanged between the agentsis limited due to communication constraints. We propose acommunication-efficient algorithm for decentralized convex optimization thatrely on sparsification of local updates exchanged between neighboring agents inthe network. In directed networks, message sparsification alterscolumn-stochasticity -- a property that plays an important role in establishingconvergence of decentralized learning tasks. We propose a decentralizedoptimization scheme that relies on local modification of mixing matrices, andshow that it achieves $\mathcal{O}(\frac{\mathrm{ln}T}{\sqrt{T}})$ convergencerate in the considered settings. Experiments validate theoretical results anddemonstrate efficacy of the proposed algorithm.

Decentralized Optimization On Time-Varying Directed Graphs Under Communication Constraints