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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

Accelerated decentralized optimization with local updates for smooth and strongly convex objectives

We study the problem of minimizing a sum of smooth and strongly convex functions split over the nodes of a network in a decentralized fashion. We propose the algorithm ESDACD, a decentralized accelerated algorithm that only requires local synchrony. Its rate depends on the condition number κ of the local functions as well as the network topology and delays. Under mild assumptions on the topology of the graph, ESDACD takes a time O((τmax+Δmax)κ/γln(ϵ-1)) to reach a precision ϵ where γ is the spectral gap of the graph, τmax the maximum communication delay and Δmax the maximum computation time. Therefore, it matches the rate of SSDA, which is optimal when τmax=ΩΔmax. Applying ESDACD to quadratic local functions leads to an accelerated randomized gossip algorithm of rate O(θ gossip /n) where θ gossip is the rate of the standard randomized gossip. To the best of our knowledge, it is the first asynchronous gossip algorithm with a provably improved rate of convergence of the second moment of the error. We illustrate these results with experiments in idealized settings.