4,567 research outputs found
Online Distributed Optimization on Dynamic Networks
This paper presents a distributed optimization scheme over a network of
agents in the presence of cost uncertainties and over switching communication
topologies. Inspired by recent advances in distributed convex optimization, we
propose a distributed algorithm based on a dual sub-gradient averaging. The
objective of this algorithm is to minimize a cost function cooperatively.
Furthermore, the algorithm changes the weights on the communication links in
the network to adapt to varying reliability of neighboring agents. A
convergence rate analysis as a function of the underlying network topology is
then presented, followed by simulation results for representative classes of
sensor networks.Comment: Submitted to The IEEE Transactions on Automatic Control, 201
Optimal Algorithms for Distributed Optimization
In this paper, we study the optimal convergence rate for distributed convex
optimization problems in networks. We model the communication restrictions
imposed by the network as a set of affine constraints and provide optimal
complexity bounds for four different setups, namely: the function F(\xb)
\triangleq \sum_{i=1}^{m}f_i(\xb) is strongly convex and smooth, either
strongly convex or smooth or just convex. Our results show that Nesterov's
accelerated gradient descent on the dual problem can be executed in a
distributed manner and obtains the same optimal rates as in the centralized
version of the problem (up to constant or logarithmic factors) with an
additional cost related to the spectral gap of the interaction matrix. Finally,
we discuss some extensions to the proposed setup such as proximal friendly
functions, time-varying graphs, improvement of the condition numbers
Distributed Adaptive Newton Methods with Globally Superlinear Convergence
This paper considers the distributed optimization problem over a network
where the global objective is to optimize a sum of local functions using only
local computation and communication. Since the existing algorithms either adopt
a linear consensus mechanism, which converges at best linearly, or assume that
each node starts sufficiently close to an optimal solution, they cannot achieve
globally superlinear convergence. To break through the linear consensus rate,
we propose a finite-time set-consensus method, and then incorporate it into
Polyak's adaptive Newton method, leading to our distributed adaptive Newton
algorithm (DAN). To avoid transmitting local Hessians, we adopt a low-rank
approximation idea to compress the Hessian and design a communication-efficient
DAN-LA. Then, the size of transmitted messages in DAN-LA is reduced to
per iteration, where is the dimension of decision vectors and is the same
as the first-order methods. We show that DAN and DAN-LA can globally achieve
quadratic and superlinear convergence rates, respectively. Numerical
experiments on logistic regression problems are finally conducted to show the
advantages over existing methods.Comment: Submitted to IEEE Transactions on Automatic Control. 14 pages, 4
figure
Multi-Dimensional Balanced Graph Partitioning via Projected Gradient Descent
Motivated by performance optimization of large-scale graph processing systems
that distribute the graph across multiple machines, we consider the balanced
graph partitioning problem. Compared to the previous work, we study the
multi-dimensional variant when balance according to multiple weight functions
is required. As we demonstrate by experimental evaluation, such
multi-dimensional balance is important for achieving performance improvements
for typical distributed graph processing workloads. We propose a new scalable
technique for the multidimensional balanced graph partitioning problem. The
method is based on applying randomized projected gradient descent to a
non-convex continuous relaxation of the objective. We show how to implement the
new algorithm efficiently in both theory and practice utilizing various
approaches for projection. Experiments with large-scale social networks
containing up to hundreds of billions of edges indicate that our algorithm has
superior performance compared with the state-of-the-art approaches
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 Convex Optimization for Continuous-Time Dynamics with Time-Varying Cost Function
In this paper, a time-varying distributed convex optimization problem is
studied for continuous-time multi-agent systems. Control algorithms are
designed for the cases of single-integrator and double-integrator dynamics. Two
discontinuous algorithms based on the signum function are proposed to solve the
problem in each case. Then in the case of double-integrator dynamics, two
continuous algorithms based on, respectively, a time-varying and a fixed
boundary layer are proposed as continuous approximations of the signum
function. Also, to account for inter-agent collision for physical agents, a
distributed convex optimization problem with swarm tracking behavior is
introduced for both single-integrator and double-integrator dynamics
Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks
We study nonconvex distributed optimization in multiagent networks where the
communications between nodes is modeled as a time-varying sequence of arbitrary
digraphs. We introduce a novel broadcast-based distributed algorithmic
framework for the (constrained) minimization of the sum of a smooth (possibly
nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a
convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually
employed to enforce some structure in the solution, typically sparsity. The
proposed method hinges on Successive Convex Approximation (SCA) techniques
coupled with i) a tracking mechanism instrumental to locally estimate the
gradients of agents' cost functions; and ii) a novel broadcast protocol to
disseminate information and distribute the computation among the agents.
Asymptotic convergence to stationary solutions is established. A key feature of
the proposed algorithm is that it neither requires the double-stochasticity of
the consensus matrices (but only column stochasticity) nor the knowledge of the
graph sequence to implement. To the best of our knowledge, the proposed
framework is the first broadcast-based distributed algorithm for convex and
nonconvex constrained optimization over arbitrary, time-varying digraphs.
Numerical results show that our algorithm outperforms current schemes on both
convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual
Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA,
US
Distributed Stochastic Approximation: Weak Convergence and Network Design
This paper studies distributed stochastic approximation algorithms based on
broadcast gossip on communication networks represented by digraphs. Weak
convergence of these algorithms is proved, and an associated ordinary
differential equation (ODE) is formulated connecting convergence points with
local objective functions and network properties. Using these results, a
methodology is proposed for network design, aimed at achieving the desired
asymptotic behavior at consensus. Convergence rate of the algorithm is also
analyzed and further improved using an attached stochastic differential
equation. Simulation results illustrate the theoretical concepts
Stochastic Optimization from Distributed, Streaming Data in Rate-limited Networks
Motivated by machine learning applications in networks of sensors,
internet-of-things (IoT) devices, and autonomous agents, we propose techniques
for distributed stochastic convex learning from high-rate data streams. The
setup involves a network of nodes---each one of which has a stream of data
arriving at a constant rate---that solve a stochastic convex optimization
problem by collaborating with each other over rate-limited communication links.
To this end, we present and analyze two algorithms---termed distributed
stochastic approximation mirror descent (D-SAMD) and accelerated distributed
stochastic approximation mirror descent (AD-SAMD)---that are based on two
stochastic variants of mirror descent and in which nodes collaborate via
approximate averaging of the local, noisy subgradients using distributed
consensus. Our main contributions are (i) bounds on the convergence rates of
D-SAMD and AD-SAMD in terms of the number of nodes, network topology, and ratio
of the data streaming and communication rates, and (ii) sufficient conditions
for order-optimum convergence of these algorithms. In particular, we show that
for sufficiently well-connected networks, distributed learning schemes can
obtain order-optimum convergence even if the communications rate is small.
Further we find that the use of accelerated methods significantly enlarges the
regime in which order-optimum convergence is achieved; this is in contrast to
the centralized setting, where accelerated methods usually offer only a modest
improvement. Finally, we demonstrate the effectiveness of the proposed
algorithms using numerical experiments.Comment: 16 pages, 6 figures; Accepted for publication in IEEE Transactions on
Signal and Information Processing over Network
Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs
We investigate the convergence rate of the recently proposed subgradient-push
method for distributed optimization over time-varying directed graphs. The
subgradient-push method can be implemented in a distributed way without
requiring knowledge of either the number of agents or the graph sequence; each
node is only required to know its out-degree at each time. Our main result is a
convergence rate of for strongly convex functions
with Lipschitz gradients even if only stochastic gradient samples are
available; this is asymptotically faster than the rate previously known for (general) convex functions
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