基于种群的增量学习算法的收敛性证明

17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'05) Pub Date : 2005-11-14 DOI:10.1109/ICTAI.2005.6

R. Rastegar, A. Hariri, M. Mazoochi

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引用次数: 12

摘要

本文提出了基于种群的增量学习(PBIL)的收敛性证明。在我们的方法中，首先，我们通过马尔可夫过程对PBIL建模，并使用常微分方程(ODE)近似其行为。然后证明相应的ODE在[0,1]n中不存在任何稳定的平稳点，n为变量个数，除了待优化函数的局部最大值。最后，我们证明了该ODE和相应的PBIL收敛于这些稳定吸引子之一。

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A Convergence Proof for the Population Based Incremental Learning Algorithm

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.

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17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'05)

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