13,464 research outputs found
Improved Runtime Bounds for the Univariate Marginal Distribution Algorithm via Anti-Concentration
Unlike traditional evolutionary algorithms which produce offspring via
genetic operators, Estimation of Distribution Algorithms (EDAs) sample
solutions from probabilistic models which are learned from selected
individuals. It is hoped that EDAs may improve optimisation performance on
epistatic fitness landscapes by learning variable interactions. However, hardly
any rigorous results are available to support claims about the performance of
EDAs, even for fitness functions without epistasis. The expected runtime of the
Univariate Marginal Distribution Algorithm (UMDA) on OneMax was recently shown
to be in by Dang and Lehre
(GECCO 2015). Later, Krejca and Witt (FOGA 2017) proved the lower bound
via an involved drift analysis.
We prove a bound, given some restrictions
on the population size. This implies the tight bound when , matching the runtime
of classical EAs. Our analysis uses the level-based theorem and
anti-concentration properties of the Poisson-Binomial distribution. We expect
that these generic methods will facilitate further analysis of EDAs.Comment: 19 pages, 1 figur
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
We construct a new framework for accelerating Markov chain Monte Carlo in
posterior sampling problems where standard methods are limited by the
computational cost of the likelihood, or of numerical models embedded therein.
Our approach introduces local approximations of these models into the
Metropolis-Hastings kernel, borrowing ideas from deterministic approximation
theory, optimization, and experimental design. Previous efforts at integrating
approximate models into inference typically sacrifice either the sampler's
exactness or efficiency; our work seeks to address these limitations by
exploiting useful convergence characteristics of local approximations. We prove
the ergodicity of our approximate Markov chain, showing that it samples
asymptotically from the \emph{exact} posterior distribution of interest. We
describe variations of the algorithm that employ either local polynomial
approximations or local Gaussian process regressors. Our theoretical results
reinforce the key observation underlying this paper: when the likelihood has
some \emph{local} regularity, the number of model evaluations per MCMC step can
be greatly reduced without biasing the Monte Carlo average. Numerical
experiments demonstrate multiple order-of-magnitude reductions in the number of
forward model evaluations used in representative ODE and PDE inference
problems, with both synthetic and real data.Comment: A major update of the theory and example
An Exponential Lower Bound for the Runtime of the cGA on Jump Functions
In the first runtime analysis of an estimation-of-distribution algorithm
(EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO
2018) proved that the runtime of the compact genetic algorithm with suitable
parameter choice on jump functions with high probability is at most polynomial
(in the dimension) if the jump size is at most logarithmic (in the dimension),
and is at most exponential in the jump size if the jump size is
super-logarithmic. The exponential runtime guarantee was achieved with a
hypothetical population size that is also exponential in the jump size.
Consequently, this setting cannot lead to a better runtime.
In this work, we show that any choice of the hypothetical population size
leads to a runtime that, with high probability, is at least exponential in the
jump size. This result might be the first non-trivial exponential lower bound
for EDAs that holds for arbitrary parameter settings.Comment: To appear in the Proceedings of FOGA 2019. arXiv admin note: text
overlap with arXiv:1903.1098
Markov Chain Analysis of Evolution Strategies on a Linear Constraint Optimization Problem
This paper analyses a -Evolution Strategy, a randomised
comparison-based adaptive search algorithm, on a simple constraint optimisation
problem. The algorithm uses resampling to handle the constraint and optimizes a
linear function with a linear constraint. Two cases are investigated: first the
case where the step-size is constant, and second the case where the step-size
is adapted using path length control. We exhibit for each case a Markov chain
whose stability analysis would allow us to deduce the divergence of the
algorithm depending on its internal parameters. We show divergence at a
constant rate when the step-size is constant. We sketch that with step-size
adaptation geometric divergence takes place. Our results complement previous
studies where stability was assumed.Comment: Amir Hussain; Zhigang Zeng; Nian Zhang. IEEE Congress on Evolutionary
Computation, Jul 2014, Beijing, Chin
Level-Based Analysis of the Population-Based Incremental Learning Algorithm
The Population-Based Incremental Learning (PBIL) algorithm uses a convex
combination of the current model and the empirical model to construct the next
model, which is then sampled to generate offspring. The Univariate Marginal
Distribution Algorithm (UMDA) is a special case of the PBIL, where the current
model is ignored. Dang and Lehre (GECCO 2015) showed that UMDA can optimise
LeadingOnes efficiently. The question still remained open if the PBIL performs
equally well. Here, by applying the level-based theorem in addition to
Dvoretzky--Kiefer--Wolfowitz inequality, we show that the PBIL optimises
function LeadingOnes in expected time for a population size , which matches the bound
of the UMDA. Finally, we show that the result carries over to BinVal, giving
the fist runtime result for the PBIL on the BinVal problem.Comment: To appea
Planar compact array with parasitic elements for MIMO systems
A compact planar array with parasitic elements is studied to be used in MIMO systems. Classical compact arrays suffer from high coupling which makes correlation and matching efficiency to be worse. A proper matching network improves these lacks although its bandwidth is low and may increase the antenna size. The proposed antenna makes use of parasitic elements to improve both correlation and efficiency. A specific software based on MoM has been developed to analyze radiating structures with several feed points. The array is optimized through a Genetic Algorithm to determine parasitic elements position in order to fulfill different figures of merit. The proposed design provides the required correlation and matching efficiency to have a good performance over a significant bandwidth
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