15 research outputs found
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Simulated annealing with noisy or imprecise energy measurements
Cover title.Includes bibliographical references.AFOSR-85-0227 DAAG-29-84-K-0005 DAAL-03-86-K-0171 Supported under a Purdue Research Initiation grant.S.B. Gelfand and S.K. Mitter ; communicated by R. Conti
Improved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets
We consider the problem of computing the minimum value of a
polynomial over a compact set , which can be
reformulated as finding a probability measure on minimizing . Lasserre showed that it suffices to consider such measures of the form
, where is a sum-of-squares polynomial and is a given
Borel measure supported on . By bounding the degree of by one gets
a converging hierarchy of upper bounds for . When is
the hypercube , equipped with the Chebyshev measure, the parameters
are known to converge to at a rate in . We
extend this error estimate to a wider class of convex bodies, while also
allowing for a broader class of reference measures, including the Lebesgue
measure. Our analysis applies to simplices, balls and convex bodies that
locally look like a ball. In addition, we show an error estimate in when satisfies a minor geometrical condition, and in when is a convex body, equipped with the Lebesgue measure. This
improves upon the currently best known error estimates in and
for these two respective cases.Comment: 30 pages with 10 figures. Update notes for second version: Added a
new section containing numerical examples that illustrate the theoretical
results -- Fixed minor mistakes/typos -- Improved some notation -- Clarified
certain explanations in the tex
General limit to thermodynamic annealing performance
Annealing has proven highly successful in finding minima in a cost landscape.
Yet, depending on the landscape, systems often converge towards local minima
rather than global ones. In this Letter, we analyse the conditions for which
annealing is approximately successful in finite time. We connect annealing to
stochastic thermodynamics to derive a general bound on the distance between the
system state at the end of the annealing and the ground state of the landscape.
This distance depends on the amount of state updates of the system and the
accumulation of non-equilibrium energy, two protocol and energy landscape
dependent quantities which we show are in a trade-off relation. We describe how
to bound the two quantities both analytically and physically. This offers a
general approach to assess the performance of annealing from accessible
parameters, both for simulated and physical implementations.Comment: 6 pages, 3 figure
Relaxing Synchronization in Distributed Simulated Annealing
This paper presents a cost error measurement scheme and relaxed synchronization method, for simulated annealing on a distributed memory multicomputer, which predicts the amount of cost error that an algorithm will tolerate. An adaptive error control method is developed and implemented on an Intel iPSC/
Metropolis-type annealing algorithms for global optimization in IRd̳
On t.p. "d̳" is superscript. Cover title.Includes bibliographical references (p. 28-29).Research supported by the Air Force Office of Scientific Research. AFOSR 89-0276by Saul B. Gelfand and Sanjoy K. Mitter
Modelling and estimation for random fields
Caption title.Includes bibliographical references (p. [21]-[22]).Supported by Air Force Office of Scientific Research. AFOSR-89-0276-C Supported by the Army Research Office. DAAL03-92-G-0115Sanjoy K. Mitter
Simulated annealing with hit-and-run for convex optimization: rigorous complexity analysis and practical perspectives for copositive programming
We give a rigorous complexity analysis of the simulated annealing algorithm
by Kalai and Vempala [Math of OR 31.2 (2006): 253-266] using the type of
temperature update suggested by Abernethy and Hazan [arXiv 1507.02528v2, 2015].
The algorithm only assumes a membership oracle of the feasible set, and we
prove that it returns a solution in polynomial time which is near-optimal with
high probability. Moreover, we propose a number of modifications to improve the
practical performance of this method, and present some numerical results for
test problems from copositive programming
Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing
Annealing is the process of gradually lowering the temperature of a system to
guide it towards its lowest energy states. In an accompanying paper [Luo et al.
Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing
performance by connecting annealing with stochastic thermodynamics tools,
including a speed-limit on state transformation from entropy production. We
here describe the derivation of the general bound in detail. In addition, we
analyze the case of simulated annealing with Glauber dynamics in depth. We show
how to bound the two case-specific quantities appearing in the bound, namely
the activity, a measure of the number of microstate jumps, and the change in
relative entropy between the state and the instantaneous thermal state, which
is due to temperature variation. We exemplify the arguments by numerical
simulations on the SK model of spin-glasses.Comment: 16 pages, 4 figure