A Hybrid-Order Distributed SGD Method for Non-Convex Optimization to Balance Communication Overhead, Computational Complexity, and Convergence Rate
This work addresses efficiency issues in distributed machine learning for non-convex problems like neural networks, offering incremental improvements over existing communication-efficient methods.
The paper tackles the challenge of balancing communication overhead, computational complexity, and convergence rate in distributed stochastic gradient descent for non-convex optimization by proposing a hybrid-order method that uses zeroth-order gradient estimation and periodic full gradient communication, achieving order-wise improvements in computational complexity while maintaining similar communication load and convergence rates as state-of-the-art methods.
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm, the worker nodes calculate and communicate some scalers, that are the directional derivatives of the sample functions in some \emph{pre-shared directions}. However, to maintain accuracy, after every specific number of iterations, they communicate the vectors of stochastic gradients. To reduce the computational complexity in each iteration, the worker nodes approximate the directional derivatives with zeroth-order stochastic gradient estimation, by performing just two function evaluations rather than computing a first-order gradient vector. The proposed method highly improves the convergence rate of the zeroth-order methods, guaranteeing order-wise faster convergence. Moreover, compared to the famous communication-efficient methods of model averaging (that perform local model updates and periodic communication of the gradients to synchronize the local models), we prove that for the general class of non-convex stochastic problems and with reasonable choice of parameters, the proposed method guarantees the same orders of communication load and convergence rate, while having order-wise less computational complexity. Experimental results on various learning problems in neural networks applications demonstrate the effectiveness of the proposed approach compared to various state-of-the-art distributed SGD methods.