1,684 research outputs found
Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging
In this paper, we study distributed big-data nonconvex optimization in
multi-agent networks. We consider the (constrained) minimization of the sum of
a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a
convex (possibly) nonsmooth regularizer. Our interest is in big-data problems
wherein there is a large number of variables to optimize. If treated by means
of standard distributed optimization algorithms, these large-scale problems may
be intractable, due to the prohibitive local computation and communication
burden at each node. We propose a novel distributed solution method whereby at
each iteration agents optimize and then communicate (in an uncoordinated
fashion) only a subset of their decision variables. To deal with non-convexity
of the cost function, the novel scheme hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a tracking mechanism
instrumental to locally estimate gradient averages; and ii) a novel block-wise
consensus-based protocol to perform local block-averaging operations and
gradient tacking. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Finally, numerical results show the
effectiveness of the proposed algorithm and highlight how the block dimension
impacts on the communication overhead and practical convergence speed
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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