5,438 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
Parallel Selective Algorithms for Big Data Optimization
We propose a decomposition framework for the parallel optimization of the sum
of a differentiable (possibly nonconvex) function and a (block) separable
nonsmooth, convex one. The latter term is usually employed to enforce structure
in the solution, typically sparsity. Our framework is very flexible and
includes both fully parallel Jacobi schemes and Gauss- Seidel (i.e.,
sequential) ones, as well as virtually all possibilities "in between" with only
a subset of variables updated at each iteration. Our theoretical convergence
results improve on existing ones, and numerical results on LASSO, logistic
regression, and some nonconvex quadratic problems show that the new method
consistently outperforms existing algorithms.Comment: This work is an extended version of the conference paper that has
been presented at IEEE ICASSP'14. The first and the second author contributed
equally to the paper. This revised version contains new numerical results on
non convex quadratic problem
D-ADMM: A Communication-Efficient Distributed Algorithm For Separable Optimization
We propose a distributed algorithm, named Distributed Alternating Direction
Method of Multipliers (D-ADMM), for solving separable optimization problems in
networks of interconnected nodes or agents. In a separable optimization problem
there is a private cost function and a private constraint set at each node. The
goal is to minimize the sum of all the cost functions, constraining the
solution to be in the intersection of all the constraint sets. D-ADMM is proven
to converge when the network is bipartite or when all the functions are
strongly convex, although in practice, convergence is observed even when these
conditions are not met. We use D-ADMM to solve the following problems from
signal processing and control: average consensus, compressed sensing, and
support vector machines. Our simulations show that D-ADMM requires less
communications than state-of-the-art algorithms to achieve a given accuracy
level. Algorithms with low communication requirements are important, for
example, in sensor networks, where sensors are typically battery-operated and
communicating is the most energy consuming operation.Comment: To appear in IEEE Transactions on Signal Processin
A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning
Learning sparse combinations is a frequent theme in machine learning. In this
paper, we study its associated optimization problem in the distributed setting
where the elements to be combined are not centrally located but spread over a
network. We address the key challenges of balancing communication costs and
optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW)
algorithm. We obtain theoretical guarantees on the optimization error
and communication cost that do not depend on the total number of
combining elements. We further show that the communication cost of dFW is
optimal by deriving a lower-bound on the communication cost required to
construct an -approximate solution. We validate our theoretical
analysis with empirical studies on synthetic and real-world data, which
demonstrate that dFW outperforms both baselines and competing methods. We also
study the performance of dFW when the conditions of our analysis are relaxed,
and show that dFW is fairly robust.Comment: Extended version of the SIAM Data Mining 2015 pape
Flexible Parallel Algorithms for Big Data Optimization
We propose a decomposition framework for the parallel optimization of the sum
of a differentiable function and a (block) separable nonsmooth, convex one. The
latter term is typically used to enforce structure in the solution as, for
example, in Lasso problems. Our framework is very flexible and includes both
fully parallel Jacobi schemes and Gauss-Seidel (Southwell-type) ones, as well
as virtually all possibilities in between (e.g., gradient- or Newton-type
methods) with only a subset of variables updated at each iteration. Our
theoretical convergence results improve on existing ones, and numerical results
show that the new method compares favorably to existing algorithms.Comment: submitted to IEEE ICASSP 201
Massively-Parallel Feature Selection for Big Data
We present the Parallel, Forward-Backward with Pruning (PFBP) algorithm for
feature selection (FS) in Big Data settings (high dimensionality and/or sample
size). To tackle the challenges of Big Data FS PFBP partitions the data matrix
both in terms of rows (samples, training examples) as well as columns
(features). By employing the concepts of -values of conditional independence
tests and meta-analysis techniques PFBP manages to rely only on computations
local to a partition while minimizing communication costs. Then, it employs
powerful and safe (asymptotically sound) heuristics to make early, approximate
decisions, such as Early Dropping of features from consideration in subsequent
iterations, Early Stopping of consideration of features within the same
iteration, or Early Return of the winner in each iteration. PFBP provides
asymptotic guarantees of optimality for data distributions faithfully
representable by a causal network (Bayesian network or maximal ancestral
graph). Our empirical analysis confirms a super-linear speedup of the algorithm
with increasing sample size, linear scalability with respect to the number of
features and processing cores, while dominating other competitive algorithms in
its class
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