2,350 research outputs found
CoCoA: A General Framework for Communication-Efficient Distributed Optimization
The scale of modern datasets necessitates the development of efficient
distributed optimization methods for machine learning. We present a
general-purpose framework for distributed computing environments, CoCoA, that
has an efficient communication scheme and is applicable to a wide variety of
problems in machine learning and signal processing. We extend the framework to
cover general non-strongly-convex regularizers, including L1-regularized
problems like lasso, sparse logistic regression, and elastic net
regularization, and show how earlier work can be derived as a special case. We
provide convergence guarantees for the class of convex regularized loss
minimization objectives, leveraging a novel approach in handling
non-strongly-convex regularizers and non-smooth loss functions. The resulting
framework has markedly improved performance over state-of-the-art methods, as
we illustrate with an extensive set of experiments on real distributed
datasets
L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework
Despite the importance of sparsity in many large-scale applications, there
are few methods for distributed optimization of sparsity-inducing objectives.
In this paper, we present a communication-efficient framework for
L1-regularized optimization in the distributed environment. By viewing
classical objectives in a more general primal-dual setting, we develop a new
class of methods that can be efficiently distributed and applied to common
sparsity-inducing models, such as Lasso, sparse logistic regression, and
elastic net-regularized problems. We provide theoretical convergence guarantees
for our framework, and demonstrate its efficiency and flexibility with a
thorough experimental comparison on Amazon EC2. Our proposed framework yields
speedups of up to 50x as compared to current state-of-the-art methods for
distributed L1-regularized optimization
A Fast Active Set Block Coordinate Descent Algorithm for -regularized least squares
The problem of finding sparse solutions to underdetermined systems of linear
equations arises in several applications (e.g. signal and image processing,
compressive sensing, statistical inference). A standard tool for dealing with
sparse recovery is the -regularized least-squares approach that has
been recently attracting the attention of many researchers. In this paper, we
describe an active set estimate (i.e. an estimate of the indices of the zero
variables in the optimal solution) for the considered problem that tries to
quickly identify as many active variables as possible at a given point, while
guaranteeing that some approximate optimality conditions are satisfied. A
relevant feature of the estimate is that it gives a significant reduction of
the objective function when setting to zero all those variables estimated
active. This enables to easily embed it into a given globally converging
algorithmic framework. In particular, we include our estimate into a block
coordinate descent algorithm for -regularized least squares, analyze
the convergence properties of this new active set method, and prove that its
basic version converges with linear rate. Finally, we report some numerical
results showing the effectiveness of the approach.Comment: 28 pages, 5 figure
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