A Convergence Proof for the Population Based Incremental Learning Algorithm

Authors:
R. Rastegar;A. Hariri;M. Mazoochi
Affiliations:
Iran Telecommunication Research Center;Iran Telecommunication Research Center;Iran Telecommunication Research Center
Venue:
ICTAI '05 Proceedings of the 17th IEEE International Conference on Tools with Artificial Intelligence
Year:
2005

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Abstract

Here we propose a convergence proof for the population based incremental learning (PBIL). In our approach, first, we model the PBIL by the Markov process and approximate its behavior using Ordinary Differential Equation (ODE). Then we prove that the corresponding ODE doesn't have any stable stationary points in [0,1]n, n is the number of variables, except the local maxima of the function to be optimized. Finally we show that this ODE and consequently the PBIL converge to one of these stable attractors.