
HAMSI: A Parallel Incremental Optimization Algorithm Using Quadratic Approximations for Solving Partially Separable Problems
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), whic...
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Parallel Coordinate Descent Methods for Big Data Optimization
In this work we show that randomized (block) coordinate descent methods ...
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RES: Regularized Stochastic BFGS Algorithm
RES, a regularized stochastic version of the BroydenFletcherGoldfarbS...
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An Analysis of Asynchronous Stochastic Accelerated Coordinate Descent
Gradient descent, and coordinate descent in particular, are core tools i...
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Random MultiConstraint Projection: Stochastic Gradient Methods for Convex Optimization with Many Constraints
Consider convex optimization problems subject to a large number of const...
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On Optimal Trees for Irregular Gather and Scatter Collectives
This paper studies the complexity of finding costoptimal communication ...
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Scalable Kernel Methods via Doubly Stochastic Gradients
The general perception is that kernel methods are not scalable, and neur...
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A Class of Parallel Doubly Stochastic Algorithms for LargeScale Learning
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We call the algorithm random parallel because it utilizes multiple parallel processors to operate on a randomly chosen subset of blocks of the feature vector. We call the algorithm stochastic because processors choose training subsets uniformly at random. Algorithms that are parallel in either of these dimensions exist, but RAPSA is the first attempt at a methodology that is parallel in both the selection of blocks and the selection of elements of the training set. In RAPSA, processors utilize the randomly chosen functions to compute the stochastic gradient component associated with a randomly chosen block. The technical contribution of this paper is to show that this minimally coordinated algorithm converges to the optimal classifier when the training objective is convex. Moreover, we present an accelerated version of RAPSA (ARAPSA) that incorporates the objective function curvature information by premultiplying the descent direction by a Hessian approximation matrix. We further extend the results for asynchronous settings and show that if the processors perform their updates without any coordination the algorithms are still convergent to the optimal argument. RAPSA and its extensions are then numerically evaluated on a linear estimation problem and a binary image classification task using the MNIST handwritten digit dataset.
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