497 research outputs found
Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization
In this work, we consider multitask learning problems where clusters of nodes
are interested in estimating their own parameter vector. Cooperation among
clusters is beneficial when the optimal models of adjacent clusters have a good
number of similar entries. We propose a fully distributed algorithm for solving
this problem. The approach relies on minimizing a global mean-square error
criterion regularized by non-differentiable terms to promote cooperation among
neighboring clusters. A general diffusion forward-backward splitting strategy
is introduced. Then, it is specialized to the case of sparsity promoting
regularizers. A closed-form expression for the proximal operator of a weighted
sum of -norms is derived to achieve higher efficiency. We also provide
conditions on the step-sizes that ensure convergence of the algorithm in the
mean and mean-square error sense. Simulations are conducted to illustrate the
effectiveness of the strategy
A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization
Based on the idea of randomized coordinate descent of -averaged
operators, a randomized primal-dual optimization algorithm is introduced, where
a random subset of coordinates is updated at each iteration. The algorithm
builds upon a variant of a recent (deterministic) algorithm proposed by V\~u
and Condat that includes the well known ADMM as a particular case. The obtained
algorithm is used to solve asynchronously a distributed optimization problem. A
network of agents, each having a separate cost function containing a
differentiable term, seek to find a consensus on the minimum of the aggregate
objective. The method yields an algorithm where at each iteration, a random
subset of agents wake up, update their local estimates, exchange some data with
their neighbors, and go idle. Numerical results demonstrate the attractive
performance of the method. The general approach can be naturally adapted to
other situations where coordinate descent convex optimization algorithms are
used with a random choice of the coordinates.Comment: 10 page
Multitask Diffusion Adaptation over Networks
Adaptive networks are suitable for decentralized inference tasks, e.g., to
monitor complex natural phenomena. Recent research works have intensively
studied distributed optimization problems in the case where the nodes have to
estimate a single optimum parameter vector collaboratively. However, there are
many important applications that are multitask-oriented in the sense that there
are multiple optimum parameter vectors to be inferred simultaneously, in a
collaborative manner, over the area covered by the network. In this paper, we
employ diffusion strategies to develop distributed algorithms that address
multitask problems by minimizing an appropriate mean-square error criterion
with -regularization. The stability and convergence of the algorithm in
the mean and in the mean-square sense is analyzed. Simulations are conducted to
verify the theoretical findings, and to illustrate how the distributed strategy
can be used in several useful applications related to spectral sensing, target
localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio
Regularized diffusion adaptation via conjugate smoothing
The purpose of this work is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cost functions are distributed across a strongly-connected network of agents and the Pareto optimal solution is sought by appealing to a multi-agent diffusion strategy. To this end, the regularizers are smoothed by means of infimal convolution and it is shown that the Pareto solution of the approximate, smooth problem can be made arbitrarily close to the solution of the original, non-smooth problem. Performance bounds are established under conditions that are weaker than assumed before in the literature, and hence applicable to a broader class of adaptation and learning problems
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