6,813 research outputs found
A Generalized Markov-Chain Modelling Approach to -ES Linear Optimization: Technical Report
Several recent publications investigated Markov-chain modelling of linear
optimization by a -ES, considering both unconstrained and linearly
constrained optimization, and both constant and varying step size. All of them
assume normality of the involved random steps, and while this is consistent
with a black-box scenario, information on the function to be optimized (e.g.
separability) may be exploited by the use of another distribution. The
objective of our contribution is to complement previous studies realized with
normal steps, and to give sufficient conditions on the distribution of the
random steps for the success of a constant step-size -ES on the
simple problem of a linear function with a linear constraint. The decomposition
of a multidimensional distribution into its marginals and the copula combining
them is applied to the new distributional assumptions, particular attention
being paid to distributions with Archimedean copulas
Sparsity-Promoting Bayesian Dynamic Linear Models
Sparsity-promoting priors have become increasingly popular over recent years
due to an increased number of regression and classification applications
involving a large number of predictors. In time series applications where
observations are collected over time, it is often unrealistic to assume that
the underlying sparsity pattern is fixed. We propose here an original class of
flexible Bayesian linear models for dynamic sparsity modelling. The proposed
class of models expands upon the existing Bayesian literature on sparse
regression using generalized multivariate hyperbolic distributions. The
properties of the models are explored through both analytic results and
simulation studies. We demonstrate the model on a financial application where
it is shown that it accurately represents the patterns seen in the analysis of
stock and derivative data, and is able to detect major events by filtering an
artificial portfolio of assets
Markov Chain Analysis of Cumulative Step-size Adaptation on a Linear Constrained Problem
This paper analyzes a (1, )-Evolution Strategy, a randomized
comparison-based adaptive search algorithm, optimizing a linear function with a
linear constraint. The algorithm uses resampling to handle the 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 cumulative step-size
adaptation. We exhibit for each case a Markov chain describing the behaviour of
the algorithm. Stability of the chain implies, by applying a law of large
numbers, either convergence or divergence of the algorithm. Divergence is the
desired behaviour. In the constant step-size case, we show stability of the
Markov chain and prove the divergence of the algorithm. In the cumulative
step-size adaptation case, we prove stability of the Markov chain in the
simplified case where the cumulation parameter equals 1, and discuss steps to
obtain similar results for the full (default) algorithm where the cumulation
parameter is smaller than 1. The stability of the Markov chain allows us to
deduce geometric divergence or convergence , depending on the dimension,
constraint angle, population size and damping parameter, at a rate that we
estimate. Our results complement previous studies where stability was assumed.Comment: Evolutionary Computation, Massachusetts Institute of Technology Press
(MIT Press): STM Titles, 201
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