2014/06/18 by Alexandre Chotard, Chotard, Alexandre, Martin Holeňa +1
Decision Sciences · Engineering · Mathematics · #Applied mathematics #Chain (unit) #Computer science #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine learning #Markov chain #Mathematical economics #Mathematical optimization #Mathematics #Neural and Evolutionary Computing (cs.NE) #Numerical Analysis (math.NA) #Physics #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1406.4619
openalex publication_date 2014/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Several recent publications investigated Markov-chain modelling of linear optimization by a (1,λ)-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 (1,λ)-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.