Parallel and distributed asynchronous adaptive stochastic gradient methods

Abstract

Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the non-adaptive versions while incurring little overhead. On the other hand, asynchronous (async) parallel computing has exhibited significantly higher speed-up over its synchronous (sync) counterpart. Async-parallel non-adaptive SGMs have been well studied in the literature from the perspectives of both theory and practical performance. Adaptive SGMs can also be implemented without much difficulty in an async-parallel way. However, to the best of our knowledge, no theoretical result of async-parallel adaptive SGMs has been established. The difficulty for analyzing adaptive SGMs with async updates originates from the second moment term. In this paper, we propose an async-parallel adaptive SGM based on AMSGrad. We show that the proposed method inherits the convergence guarantee of AMSGrad for both convex and non-convex problems, if the staleness (also called delay) caused by asynchrony is bounded. Our convergence rate results indicate a nearly linear parallelization speed-up if $\tau =o(K^{\frac{1}{4}})$, where $\tau$ is the staleness and $K$ is the number of iterations. The proposed method is tested on both convex and non-convex machine learning problems, and the numerical results demonstrate its clear advantages over the sync counterpart and the async-parallel nonadaptive SGM.

References in corpus (14)

• Adam: A Method for Stochastic Optimization
• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• On the Convergence of Adam and Beyond
• HOGWILD!: A Lock-Free Approach to Parallelizing Stochastic Gradient Descent
• Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization
• Revisiting Small Batch Training for Deep Neural Networks
• ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates
• Adaptive Gradient Methods with Dynamic Bound of Learning Rate
• An Asynchronous Parallel Stochastic Coordinate Descent Algorithm
• On the Convergence Proof of AMSGrad and a New Version
• Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks
• On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization
• Improved asynchronous parallel optimization analysis for stochastic incremental methods
• Convergence Analyses of Online ADAM Algorithm in Convex Setting and Two-Layer ReLU Neural Network

Cited by in corpus (1)

• Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization