LevelBased Analysis of the PopulationBased Incremental Learning Algorithm
Abstract
The PopulationBased 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 levelbased theorem in addition to DvoretzkyKieferWolfowitz inequality, we show that the PBIL optimises function LeadingOnes in expected time $\mathcal{O}(n\lambda \log \lambda + n^2)$ for a population size $\lambda = \Omega(\log n)$, 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.01710
 Bibcode:
 2018arXiv180601710L
 Keywords:

 Computer Science  Neural and Evolutionary Computing
 EPrint:
 To appear