D-SPIDER-SFO: A Decentralized Optimization Algorithm with Faster Convergence Rate for Nonconvex Problems

Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator Stochastic First-Order method (SPIDER-SFO) nearly achieves the algorithmic lower bound in certain regimes for nonconvex problems. However, whether we can find a decentralized algorithm which achieves a similar convergence rate to SPIDER-SFO is still unclear. To tackle this problem, we propose a decentralized variant of SPIDER-SFO, called decentralized SPIDER-SFO (D-SPIDER-SFO). We show that D-SPIDER-SFO achieves a similar gradient computation cost-- that is, O ( null 3) for finding an null -approximate first-order stationary point--to its centralized counterpart. To the best of our knowledge, D-SPIDER-SFO achieves the state-of-the-art performance for solving nonconvex optimization problems on decentralized networks in terms of the computational cost. Experiments on different network configurations demonstrate the efficiency of the proposed method. Introduction Distributed optimization is a popular technique for solving large scale machine learning problems Li et al. (2014), ranging from visual object recognition Huang et al. (2017); He et al. (2016) to natural language processing V aswani et al. (2017); Devlin et al. (2019). For distributed optimization, a set of workers form a connected computational network, and each worker is assigned a portion of the computing task. The centralized network topology, like parameter server Jianmin et al. (2016); Dean et al. (2012); Li et al. (2014); Zinkevich et al. (2010), consists of a central worker connected with all other workers.