1,813 research outputs found

    Asynchronous Optimization Methods for Efficient Training of Deep Neural Networks with Guarantees

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    Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees exist beyond cases where closed-form proximal operator solutions are available. As most popular contemporary deep neural networks lead to nonsmooth and nonconvex objectives, there is now a pressing need for such convergence guarantees. In this paper, we analyze for the first time the convergence of stochastic asynchronous optimization for this general class of objectives. In particular, we focus on stochastic subgradient methods allowing for block variable partitioning, where the shared-memory-based model is asynchronously updated by concurrent processes. To this end, we first introduce a probabilistic model which captures key features of real asynchronous scheduling between concurrent processes; under this model, we establish convergence with probability one to an invariant set for stochastic subgradient methods with momentum. From the practical perspective, one issue with the family of methods we consider is that it is not efficiently supported by machine learning frameworks, as they mostly focus on distributed data-parallel strategies. To address this, we propose a new implementation strategy for shared-memory based training of deep neural networks, whereby concurrent parameter servers are utilized to train a partitioned but shared model in single- and multi-GPU settings. Based on this implementation, we achieve on average 1.2x speed-up in comparison to state-of-the-art training methods for popular image classification tasks without compromising accuracy

    Stochastic Block Mirror Descent Methods for Nonsmooth and Stochastic Optimization

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    In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significantly reduce the cost per iteration of the latter algorithm. We establish the rate of convergence of the SBMD method along with its associated large-deviation results for solving general nonsmooth and stochastic optimization problems. We also introduce different variants of this method and establish their rate of convergence for solving strongly convex, smooth, and composite optimization problems, as well as certain nonconvex optimization problems. To the best of our knowledge, all these developments related to the SBMD methods are new in the stochastic optimization literature. Moreover, some of our results also seem to be new for block coordinate descent methods for deterministic optimization
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