An Asynchronous Parallel Approach to Sparse Recovery

Asynchronous parallel computing and sparse recovery are two areas that have received recent interest. Asynchronous algorithms are often studied to solve optimization problems where the cost function takes the form $\sum_{i=1}^M f_i(x)$, with a common assumption that each $f_i$ is sparse; that is, each $f_i$ acts only on a small number of components of $x\in\mathbb{R}^n$. Sparse recovery problems, such as compressed sensing, can be formulated as optimization problems, however, the cost functions $f_i$ are dense with respect to the components of $x$, and instead the signal $x$ is assumed to be sparse, meaning that it has only $s$ non-zeros where $s\ll n$. Here we address how one may use an asynchronous parallel architecture when the cost functions $f_i$ are not sparse in $x$, but rather the signal $x$ is sparse. We propose an asynchronous parallel approach to sparse recovery via a stochastic greedy algorithm, where multiple processors asynchronously update a vector in shared memory containing information on the estimated signal support. We include numerical simulations that illustrate the potential benefits of our proposed asynchronous method.Comment: 5 pages, 2 figure

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

Parallel coordinate descent for the Adaboost problem

We design a randomised parallel version of Adaboost based on previous studies on parallel coordinate descent. The algorithm uses the fact that the logarithm of the exponential loss is a function with coordinate-wise Lipschitz continuous gradient, in order to define the step lengths. We provide the proof of convergence for this randomised Adaboost algorithm and a theoretical parallelisation speedup factor. We finally provide numerical examples on learning problems of various sizes that show that the algorithm is competitive with concurrent approaches, especially for large scale problems.Comment: 7 pages, 3 figures, extended version of the paper presented to ICMLA'1