Decentralized Optimization in Networks with Arbitrary Delays

We consider the problem of decentralized optimization in networks with communication delays. To accommodate delays, we need decentralized optimization algorithms that work on directed graphs. Existing approaches require nodes to know their out-degree to achieve convergence. We propose a novel gossip-based algorithm that circumvents this requirement, allowing decentralized optimization in networks with communication delays. We prove that our algorithm converges on non-convex objectives, with the same main complexity order term as centralized Stochastic Gradient Descent (SGD), and show that the graph topology and the delays only affect the higher order terms. We provide numerical simulations that illustrate our theoretical results.