TY - GEN
T1 - Level-based analysis of the population-based incremental learning algorithm
AU - Lehre, Per Kristian
AU - Nguyen, Phan Trung Hai
PY - 2018/10/5
Y1 - 2018/10/5
N2 - 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 LEADINGONES in expected time O (nλ log λ + n2) for a population size λ = Ω(log n), which matches the bound of the UMDA. Finally, we showthat the result carries over to BINVAL giving the fist runtime result for the PBIL on the BINVAL problem.the bound of the UMDA. Finally,we show that the result carries over to BinVal
AB - 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 LEADINGONES in expected time O (nλ log λ + n2) for a population size λ = Ω(log n), which matches the bound of the UMDA. Finally, we showthat the result carries over to BINVAL giving the fist runtime result for the PBIL on the BINVAL problem.the bound of the UMDA. Finally,we show that the result carries over to BinVal
KW - population-based incremental learning
KW - LeadingOnes
KW - BinVal
KW - running time analysis
KW - level-based analysis
KW - theory
U2 - 10.1007/978-3-319-99253-2
DO - 10.1007/978-3-319-99253-2
M3 - Conference contribution
SN - 978-3-319-99252-5
VL - 11101
T3 - Lecture Notes in Computer Science
BT - Proceedings of the 15th International Conference on Parallel Problem Solving from Nature 2018 (PPSN XV)
PB - Springer
T2 - 15th International Conference on Parallel Problem Solving from Nature 2018 (PPSN XV)
Y2 - 8 September 2018 through 12 September 2018
ER -