2,491 research outputs found
SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives
In this work we introduce a new optimisation method called SAGA in the spirit
of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient
algorithms with fast linear convergence rates. SAGA improves on the theory
behind SAG and SVRG, with better theoretical convergence rates, and has support
for composite objectives where a proximal operator is used on the regulariser.
Unlike SDCA, SAGA supports non-strongly convex problems directly, and is
adaptive to any inherent strong convexity of the problem. We give experimental
results showing the effectiveness of our method.Comment: Advances In Neural Information Processing Systems, Nov 2014,
Montreal, Canad
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
SCOPE: Scalable Composite Optimization for Learning on Spark
Many machine learning models, such as logistic regression~(LR) and support
vector machine~(SVM), can be formulated as composite optimization problems.
Recently, many distributed stochastic optimization~(DSO) methods have been
proposed to solve the large-scale composite optimization problems, which have
shown better performance than traditional batch methods. However, most of these
DSO methods are not scalable enough. In this paper, we propose a novel DSO
method, called \underline{s}calable \underline{c}omposite
\underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it
on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both
computation-efficient and communication-efficient. Theoretical analysis shows
that SCOPE is convergent with linear convergence rate when the objective
function is convex. Furthermore, empirical results on real datasets show that
SCOPE can outperform other state-of-the-art distributed learning methods on
Spark, including both batch learning methods and DSO methods
Distributed Machine Learning via Sufficient Factor Broadcasting
Matrix-parametrized models, including multiclass logistic regression and
sparse coding, are used in machine learning (ML) applications ranging from
computer vision to computational biology. When these models are applied to
large-scale ML problems starting at millions of samples and tens of thousands
of classes, their parameter matrix can grow at an unexpected rate, resulting in
high parameter synchronization costs that greatly slow down distributed
learning. To address this issue, we propose a Sufficient Factor Broadcasting
(SFB) computation model for efficient distributed learning of a large family of
matrix-parameterized models, which share the following property: the parameter
update computed on each data sample is a rank-1 matrix, i.e., the outer product
of two "sufficient factors" (SFs). By broadcasting the SFs among worker
machines and reconstructing the update matrices locally at each worker, SFB
improves communication efficiency --- communication costs are linear in the
parameter matrix's dimensions, rather than quadratic --- without affecting
computational correctness. We present a theoretical convergence analysis of
SFB, and empirically corroborate its efficiency on four different
matrix-parametrized ML models
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