216 research outputs found
Distributed Stochastic Optimization over Time-Varying Noisy Network
This paper is concerned with distributed stochastic multi-agent optimization
problem over a class of time-varying network with slowly decreasing
communication noise effects. This paper considers the problem in composite
optimization setting which is more general in noisy network optimization. It is
noteworthy that existing methods for noisy network optimization are Euclidean
projection based. We present two related different classes of non-Euclidean
methods and investigate their convergence behavior. One is distributed
stochastic composite mirror descent type method (DSCMD-N) which provides a more
general algorithm framework than former works in this literature. As a
counterpart, we also consider a composite dual averaging type method (DSCDA-N)
for noisy network optimization. Some main error bounds for DSCMD-N and DSCDA-N
are obtained. The trade-off among stepsizes, noise decreasing rates,
convergence rates of algorithm is analyzed in detail. To the best of our
knowledge, this is the first work to analyze and derive convergence rates of
optimization algorithm in noisy network optimization. We show that an optimal
rate of in nonsmooth convex optimization can be obtained for
proposed methods under appropriate communication noise condition. Moveover,
convergence rates in different orders are comprehensively derived in both
expectation convergence and high probability convergence sense.Comment: 27 page
Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients
This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance
Improved Dynamic Regret of Distributed Online Multiple Frank-Wolfe Convex Optimization
In this paper, we consider a distributed online convex optimization problem
over a time-varying multi-agent network. The goal of this network is to
minimize a global loss function through local computation and communication
with neighbors. To effectively handle the optimization problem with a
high-dimensional and structural constraint set, we develop a distributed online
multiple Frank-Wolfe algorithm to avoid the expensive computational cost of
projection operation. The dynamic regret bounds are established as
with the linear oracle number , which depends on the horizon (total iteration number) , the
function variation , and the tuning parameter . In particular,
when the prior knowledge of and is available, the bound can be
enhanced to . Moreover, we illustrate the significant
advantages of the multiple iteration technique and reveal a trade-off between
dynamic regret bound, computational cost, and communication cost. Finally, the
performance of our algorithm is verified and compared through the distributed
online ridge regression problems with two constraint sets
Distributed Solvers for Network Linear Equations with Scalarized Compression
In this paper, we study distributed solvers for network linear equations over
a network with node-to-node communication messages compressed as scalar values.
Our key idea lies in a dimension compression scheme including a dimension
compressing vector that applies to individual node states to generate a
real-valued message for node communication as an inner product, and a data
unfolding step in the local computations where the scalar message is plotted
along the subspace generated by the compression vector. We first present a
compressed average consensus flow that relies only on such scalar
communication, and show that exponential convergence can be achieved with well
excited signals for the compression vector. We then employ such a compressed
consensus flow as a fundamental consensus subroutine to develop distributed
continuous-time and discrete-time solvers for network linear equations, and
prove their exponential convergence properties under scalar node
communications. With scalar communications, a direct benefit would be the
reduced node-to-node communication channel capacity requirement for distributed
computing. Numerical examples are presented to illustrate the effectiveness of
the established theoretical results.Comment: 8 pages, 4 figure
Atmospheric circulation of hot Jupiters: Coupled radiative-dynamical general circulation model simulations of HD 189733b and HD 209458b
We present global, three-dimensional numerical simulations of HD 189733b and
HD 209458b that couple the atmospheric dynamics to a realistic representation
of non-gray cloud-free radiative transfer. The model, which we call the
Substellar and Planetary Atmospheric Radiation and Circulation (SPARC) model,
adopts the MITgcm for the dynamics and uses the radiative model of McKay,
Marley, Fortney, and collaborators for the radiation. Like earlier work with
simplified forcing, our simulations develop a broad eastward equatorial jet,
mean westward flow at higher latitudes, and substantial flow over the poles at
low pressure. For HD 189733b, our simulations without TiO and VO opacity can
explain the broad features of the observed 8 and 24-micron light curves,
including the modest day-night flux variation and the fact that the planet/star
flux ratio peaks before the secondary eclipse. Our simulations also provide
reasonable matches to the Spitzer secondary-eclipse depths at 4.5, 5.8, 8, 16,
and 24 microns and the groundbased upper limit at 2.2 microns. However, we
substantially underpredict the 3.6-micron secondary-eclipse depth, suggesting
that our simulations are too cold in the 0.1-1 bar region. Predicted temporal
variability in secondary-eclipse depths is ~1% at Spitzer bandpasses,
consistent with recent observational upper limits at 8 microns. We also show
that nonsynchronous rotation can significantly alter the jet structure. For HD
209458b, we include TiO and VO opacity; these simulations develop a hot (>2000
K) dayside stratosphere. Despite this stratosphere, we do not reproduce current
Spitzer photometry of this planet. Light curves in Spitzer bandpasses show
modest phase variation and satisfy the observational upper limit on day-night
phase variation at 8 microns. (abridged)Comment: 20 pages (emulate-apj format), 21 figures, final version now
published in ApJ. Includes expanded discussion of radiative-transfer methods
and two new figure
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