Asynchronous Distributed Semi-Stochastic Gradient Optimization

With the recent proliferation of large-scale learning problems,there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However, existing algorithms either suffer from slow convergence due to the inherent variance of stochastic gradients, or have a fast linear convergence rate but at the expense of poorer solution quality. In this paper, we combine their merits by proposing a fast distributed asynchronous SGD-based algorithm with variance reduction. A constant learning rate can be used, and it is also guaranteed to converge linearly to the optimal solution. Experiments on the Google Cloud Computing Platform demonstrate that the proposed algorithm outperforms state-of-the-art distributed asynchronous algorithms in terms of both wall clock time and solution quality

Breaking the Nonsmooth Barrier: A Scalable Parallel Method for Composite Optimization

Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet, despite their practical success, support for nonsmooth objectives is still lacking, making them unsuitable for many problems of interest in machine learning, such as the Lasso, group Lasso or empirical risk minimization with convex constraints. In this work, we propose and analyze ProxASAGA, a fully asynchronous sparse method inspired by SAGA, a variance reduced incremental gradient algorithm. The proposed method is easy to implement and significantly outperforms the state of the art on several nonsmooth, large-scale problems. We prove that our method achieves a theoretical linear speedup with respect to the sequential version under assumptions on the sparsity of gradients and block-separability of the proximal term. Empirical benchmarks on a multi-core architecture illustrate practical speedups of up to 12x on a 20-core machine.Comment: Appears in Advances in Neural Information Processing Systems 30 (NIPS 2017), 28 page