A hybrid variance-reduced method for decentralized stochastic non-convex optimization
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This paper considers decentralized stochastic optimization over a network of n nodes, where each node possesses a smooth non-convex local cost function and the goal of the networked nodes is to find an ϵ-accurate first-order stationary point of the sum of the local costs. We focus on an online setting, where each node accesses its local cost only by means of a stochastic first-order oracle that returns a noisy version of the exact gradient. In this context, we propose a novel single-loop decentralized hybrid variance-reduced stochastic gradient method, called , that outperforms the existing approaches in terms of both the oracle complexity and practical implementation. The algorithm implements specialized local hybrid stochastic gradient estimators that are fused over the network to track the global gradient. Remarkably, achieves a network-independent oracle complexity of O(n^-1ϵ^-3) when the required error tolerance ϵ is small enough, leading to a linear speedup with respect to the centralized optimal online variance-reduced approaches that operate on a single node. Numerical experiments are provided to illustrate our main technical results.
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