5,839 research outputs found
Asynchronous Decentralized Optimization in Directed Networks
A popular asynchronous protocol for decentralized optimization is randomized
gossip where a pair of neighbors concurrently update via pairwise averaging. In
practice, this creates deadlocks and is vulnerable to information delays. It
can also be problematic if a node is unable to response or has only access to
its private-preserved local dataset. To address these issues simultaneously,
this paper proposes an asynchronous decentralized algorithm, i.e. APPG, with
{\em directed} communication where each node updates {\em asynchronously} and
independently of any other node. If local functions are strongly-convex with
Lipschitz-continuous gradients, each node of APPG converges to the same optimal
solution at a rate of , where and the virtual
counter increases by 1 no matter on which node updates. The superior
performance of APPG is validated on a logistic regression problem against
state-of-the-art methods in terms of linear speedup and system implementations
Push-Pull Gradient Methods for Distributed Optimization in Networks
In this paper, we focus on solving a distributed convex optimization problem
in a network, where each agent has its own convex cost function and the goal is
to minimize the sum of the agents' cost functions while obeying the network
connectivity structure. In order to minimize the sum of the cost functions, we
consider new distributed gradient-based methods where each node maintains two
estimates, namely, an estimate of the optimal decision variable and an estimate
of the gradient for the average of the agents' objective functions. From the
viewpoint of an agent, the information about the gradients is pushed to the
neighbors, while the information about the decision variable is pulled from the
neighbors hence giving the name "push-pull gradient methods". The methods
utilize two different graphs for the information exchange among agents, and as
such, unify the algorithms with different types of distributed architecture,
including decentralized (peer-to-peer), centralized (master-slave), and
semi-centralized (leader-follower) architecture. We show that the proposed
algorithms and their many variants converge linearly for strongly convex and
smooth objective functions over a network (possibly with unidirectional data
links) in both synchronous and asynchronous random-gossip settings. In
particular, under the random-gossip setting, "push-pull" is the first class of
algorithms for distributed optimization over directed graphs. Moreover, we
numerically evaluate our proposed algorithms in both scenarios, and show that
they outperform other existing linearly convergent schemes, especially for
ill-conditioned problems and networks that are not well balanced.Comment: Parts of the results appear in Proceedings of the 57th IEEE
Conference on Decision and Control (see arXiv:1803.07588
A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks
In this paper, we consider the problem of distributed consensus optimization
over multi-agent networks with directed network topology. Assuming each agent
has a local cost function that is smooth and strongly convex, the global
objective is to minimize the average of all the local cost functions. To solve
the problem, we introduce a robust gradient tracking method (R-Push-Pull)
adapted from the recently proposed Push-Pull/AB algorithm. R-Push-Pull inherits
the advantages of Push-Pull and enjoys linear convergence to the optimal
solution with exact communication. Under noisy information exchange,
R-Push-Pull is more robust than the existing gradient tracking based
algorithms; the solutions obtained by each agent reach a neighborhood of the
optimum in expectation exponentially fast under a constant stepsize policy. We
provide a numerical example that demonstrate the effectiveness of R-Push-Pull
Toward Creating Subsurface Camera
In this article, the framework and architecture of Subsurface Camera (SAMERA)
is envisioned and described for the first time. A SAMERA is a geophysical
sensor network that senses and processes geophysical sensor signals, and
computes a 3D subsurface image in-situ in real-time. The basic mechanism is:
geophysical waves propagating/reflected/refracted through subsurface enter a
network of geophysical sensors, where a 2D or 3D image is computed and
recorded; a control software may be connected to this network to allow view of
the 2D/3D image and adjustment of settings such as resolution, filter,
regularization and other algorithm parameters. System prototypes based on
seismic imaging have been designed. SAMERA technology is envisioned as a game
changer to transform many subsurface survey and monitoring applications,
including oil/gas exploration and production, subsurface infrastructures and
homeland security, wastewater and CO2 sequestration, earthquake and volcano
hazard monitoring. The system prototypes for seismic imaging have been built.
Creating SAMERA requires an interdisciplinary collaboration and transformation
of sensor networks, signal processing, distributed computing, and geophysical
imaging.Comment: 15 pages, 7 figure
Approximate Projection Methods for Decentralized Optimization with Functional Constraints
We consider distributed convex optimization problems that involve a separable
objective function and nontrivial functional constraints, such as Linear Matrix
Inequalities (LMIs). We propose a decentralized and computationally inexpensive
algorithm which is based on the concept of approximate projections. Our
algorithm is one of the consensus based methods in that, at every iteration,
each agent performs a consensus update of its decision variables followed by an
optimization step of its local objective function and local constraints. Unlike
other methods, the last step of our method is not an Euclidean projection onto
the feasible set, but instead a subgradient step in the direction that
minimizes the local constraint violation. We propose two different averaging
schemes to mitigate the disagreements among the agents' local estimates. We
show that the algorithms converge almost surely, i.e., every agent agrees on
the same optimal solution, under the assumption that the objective functions
and constraint functions are nondifferentiable and their subgradients are
bounded. We provide simulation results on a decentralized optimal gossip
averaging problem, which involves SDP constraints, to complement our
theoretical results
A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates
This paper proposes a novel proximal-gradient algorithm for a decentralized
optimization problem with a composite objective containing smooth and
non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with
by gradient and proximal updates, respectively. The proposed algorithm is
closely related to a previous algorithm, PG-EXTRA \cite{shi2015proximal}, but
has a few advantages. First of all, agents use uncoordinated step-sizes, and
the stable upper bounds on step-sizes are independent of network topologies.
The step-sizes depend on local objective functions, and they can be as large as
those of the gradient descent. Secondly, for the special case without
non-smooth terms, linear convergence can be achieved under the strong convexity
assumption. The dependence of the convergence rate on the objective functions
and the network are separated, and the convergence rate of the new algorithm is
as good as one of the two convergence rates that match the typical rates for
the general gradient descent and the consensus averaging. We provide numerical
experiments to demonstrate the efficacy of the introduced algorithm and
validate our theoretical discoveries
Asynchronous Decentralized 20 Questions for Adaptive Search
This paper considers the problem of adaptively searching for an unknown
target using multiple agents connected through a time-varying network topology.
Agents are equipped with sensors capable of fast information processing, and we
propose a decentralized collaborative algorithm for controlling their search
given noisy observations. Specifically, we propose decentralized extensions of
the adaptive query-based search strategy that combines elements from the 20
questions approach and social learning. Under standard assumptions on the
time-varying network dynamics, we prove convergence to correct consensus on the
value of the parameter as the number of iterations go to infinity. The
convergence analysis takes a novel approach using martingale-based techniques
combined with spectral graph theory. Our results establish that stability and
consistency can be maintained even with one-way updating and randomized
pairwise averaging, thus providing a scalable low complexity method with
performance guarantees. We illustrate the effectiveness of our algorithm for
random network topologies.Comment: 19 pages, Submitted. arXiv admin note: substantial text overlap with
arXiv:1312.784
Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions
We consider the standard model of distributed optimization of a sum of
functions F(\bz) = \sum_{i=1}^n f_i(\bz), where node in a network holds
the function f_i(\bz). We allow for a harsh network model characterized by
asynchronous updates, message delays, unpredictable message losses, and
directed communication among nodes. In this setting, we analyze a modification
of the Gradient-Push method for distributed optimization, assuming that
\begin{enumerate*}[label=(\roman*)] \item node is capable of generating
gradients of its function f_i(\bz) corrupted by zero-mean bounded-support
additive noise at each step, \item F(\bz) is strongly convex, and \item each
f_i(\bz) has Lipschitz gradients. We show that our proposed method
asymptotically performs as well as the best bounds on centralized gradient
descent that takes steps in the direction of the sum of the noisy gradients of
all the functions f_1(\bz), \ldots, f_n(\bz) at each step
Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs
This paper considers the problem of distributed optimization over
time-varying graphs. For the case of undirected graphs, we introduce a
distributed algorithm, referred to as DIGing, based on a combination of a
distributed inexact gradient method and a gradient tracking technique. The
DIGing algorithm uses doubly stochastic mixing matrices and employs fixed
step-sizes and, yet, drives all the agents' iterates to a global and consensual
minimizer. When the graphs are directed, in which case the implementation of
doubly stochastic mixing matrices is unrealistic, we construct an algorithm
that incorporates the push-sum protocol into the DIGing structure, thus
obtaining Push-DIGing algorithm. The Push-DIGing uses column stochastic
matrices and fixed step-sizes, but it still converges to a global and
consensual minimizer. Under the strong convexity assumption, we prove that the
algorithms converge at R-linear (geometric) rates as long as the step-sizes do
not exceed some upper bounds. We establish explicit estimates for the
convergence rates. When the graph is undirected it shows that DIGing scales
polynomially in the number of agents. We also provide some numerical
experiments to demonstrate the efficacy of the proposed algorithms and to
validate our theoretical findings
Distributed Nesterov gradient methods over arbitrary graphs
In this letter, we introduce a distributed Nesterov method, termed as
, that does not require doubly-stochastic weight matrices.
Instead, the implementation is based on a simultaneous application of both row-
and column-stochastic weights that makes this method applicable to arbitrary
(strongly-connected) graphs. Since constructing column-stochastic weights needs
additional information (the number of outgoing neighbors at each agent), not
available in certain communication protocols, we derive a variation, termed as
FROZEN, that only requires row-stochastic weights but at the expense of
additional iterations for eigenvector learning. We numerically study these
algorithms for various objective functions and network parameters and show that
the proposed distributed Nesterov methods achieve acceleration compared to the
current state-of-the-art methods for distributed optimization
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