31,241 research outputs found
Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks
We study diffusion and consensus based optimization of a sum of unknown
convex objective functions over distributed networks. The only access to these
functions is through stochastic gradient oracles, each of which is only
available at a different node, and a limited number of gradient oracle calls is
allowed at each node. In this framework, we introduce a convex optimization
algorithm based on the stochastic gradient descent (SGD) updates. Particularly,
we use a carefully designed time-dependent weighted averaging of the SGD
iterates, which yields a convergence rate of
after gradient updates for each node on
a network of nodes. We then show that after gradient oracle calls, the
average SGD iterate achieves a mean square deviation (MSD) of
. This rate of convergence is optimal as it
matches the performance lower bound up to constant terms. Similar to the SGD
algorithm, the computational complexity of the proposed algorithm also scales
linearly with the dimensionality of the data. Furthermore, the communication
load of the proposed method is the same as the communication load of the SGD
algorithm. Thus, the proposed algorithm is highly efficient in terms of
complexity and communication load. We illustrate the merits of the algorithm
with respect to the state-of-art methods over benchmark real life data sets and
widely studied network topologies
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
Distributed Clustering and Learning Over Networks
Distributed processing over networks relies on in-network processing and
cooperation among neighboring agents. Cooperation is beneficial when agents
share a common objective. However, in many applications agents may belong to
different clusters that pursue different objectives. Then, indiscriminate
cooperation will lead to undesired results. In this work, we propose an
adaptive clustering and learning scheme that allows agents to learn which
neighbors they should cooperate with and which other neighbors they should
ignore. In doing so, the resulting algorithm enables the agents to identify
their clusters and to attain improved learning and estimation accuracy over
networks. We carry out a detailed mean-square analysis and assess the error
probabilities of Types I and II, i.e., false alarm and mis-detection, for the
clustering mechanism. Among other results, we establish that these
probabilities decay exponentially with the step-sizes so that the probability
of correct clustering can be made arbitrarily close to one.Comment: 47 pages, 6 figure
Distributed Coupled Multi-Agent Stochastic Optimization
This work develops effective distributed strategies for the solution of
constrained multi-agent stochastic optimization problems with coupled
parameters across the agents. In this formulation, each agent is influenced by
only a subset of the entries of a global parameter vector or model, and is
subject to convex constraints that are only known locally. Problems of this
type arise in several applications, most notably in disease propagation models,
minimum-cost flow problems, distributed control formulations, and distributed
power system monitoring. This work focuses on stochastic settings, where a
stochastic risk function is associated with each agent and the objective is to
seek the minimizer of the aggregate sum of all risks subject to a set of
constraints. Agents are not aware of the statistical distribution of the data
and, therefore, can only rely on stochastic approximations in their learning
strategies. We derive an effective distributed learning strategy that is able
to track drifts in the underlying parameter model. A detailed performance and
stability analysis is carried out showing that the resulting coupled diffusion
strategy converges at a linear rate to an neighborhood of the true
penalized optimizer
Distributed Diffusion-Based LMS for Node-Specific Adaptive Parameter Estimation
A distributed adaptive algorithm is proposed to solve a node-specific
parameter estimation problem where nodes are interested in estimating
parameters of local interest, parameters of common interest to a subset of
nodes and parameters of global interest to the whole network. To address the
different node-specific parameter estimation problems, this novel algorithm
relies on a diffusion-based implementation of different Least Mean Squares
(LMS) algorithms, each associated with the estimation of a specific set of
local, common or global parameters. Coupled with the estimation of the
different sets of parameters, the implementation of each LMS algorithm is only
undertaken by the nodes of the network interested in a specific set of local,
common or global parameters. The study of convergence in the mean sense reveals
that the proposed algorithm is asymptotically unbiased. Moreover, a
spatial-temporal energy conservation relation is provided to evaluate the
steady-state performance at each node in the mean-square sense. Finally, the
theoretical results and the effectiveness of the proposed technique are
validated through computer simulations in the context of cooperative spectrum
sensing in Cognitive Radio networks.Comment: 13 pages, 6 figure
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