  We consider the task of decentralized minimization of the sum of smooth
strongly convex functions stored across the nodes of a network. For this
problem, lower bounds on the number of gradient computations and the number of
communication rounds required to achieve $\varepsilon$ accuracy have recently
been proven. We propose two new algorithms for this decentralized optimization
problem and equip them with complexity guarantees. We show that our first
method is optimal both in terms of the number of communication rounds and in
terms of the number of gradient computations. Unlike existing optimal
algorithms, our algorithm does not rely on the expensive evaluation of dual
gradients. Our second algorithm is optimal in terms of the number of
communication rounds, without a logarithmic factor. Our approach relies on
viewing the two proposed algorithms as accelerated variants of the Forward
Backward algorithm to solve monotone inclusions associated with the
decentralized optimization problem. We also verify the efficacy of our methods
against state-of-the-art algorithms through numerical experiments.
