On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization

By Hao Yu, Rong Jin. 2019

53 citations recorded by the source corpus.

For SGD based distributed stochastic optimization, computation complexity, measured by the convergence rate in terms of the number of stochastic gradient calls, and communication complexity, measured by the number of inter-node communication rounds, are two most important performance metrics. The classical data-parallel implementation of SGD over $N$ workers can achieve linear speedup of its convergence rate but incurs an inter-node communication round at each batch. We study the benefit of using dynamically increasing batch sizes in parallel SGD for stochastic non-convex optimization by charactering the attained convergence rate and the required number of communication rounds. We show that for stochastic non-convex optimization under the P-L condition, the classical data-parallel SGD with exponentially increasing batch sizes can achieve the fastest known $O(1/(NT))$ convergence with linear speedup using only $\log(T)$ communication rounds. For general stochastic non-convex optimization, we propose a Catalyst-like algorithm to achieve the fastest known $O(1/\sqrt{NT})$ convergence with only $O(\sqrt{NT}\log(\frac{T}{N}))$ communication rounds.

Subfields: Artificial Intelligence, Computational Mechanics

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Citations in the corpus

Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization (2019, methodology): “While the algorithm of [42] provides a different way of reducing communication in distributed setting, for a large number of iterations, their algorithm will require large mini-”