Function Approximation With XCS: Hyperellipsoidal Conditions, Recursive Least Squares, and Compaction
Function Approximation With XCS: Hyperellipsoidal Conditions, Recursive Least Squares, and Compaction
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使用 XCS 进行函数逼近：超椭球条件、递归最小二乘法和压缩
DOI：
10.1109/tevc.2007.903551
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发表时间：
2008
影响因子：
14.3
通讯作者：
Stewart W. Wilson
中科院分区：
文献类型：
--
作者：
Martin Volker Butz;P. Lanzi;Stewart W. Wilson
学习分类器系统(LCS)的一个重要优点在于结合了遗传优化技术和基于梯度的逼近技术。所选择的近似技术发展了局部最优近似，例如精确的分类估计、Q值预测或线性函数近似。遗传优化技术旨在将这些局部近似有效地分布在问题空间中。这两个组件共同开发了一个分布式的、本地优化的问题解决方案，其形式是一组专家规则，通常称为分类器。在函数逼近问题中，XCSF分类器系统以重叠、分段线性逼近的形式开发问题解决方案。本文表明，XCSF在函数逼近问题上的性能还得益于：1)改进的表示法；2)改进的遗传算子；以及3)改进的逼近技术。此外，本文还引入了一种新的最接近分类器匹配机制来有效地压缩XCS的最终问题解。由此产生的紧凑机制可以将种群规模平均缩减90%，而预测精度仅略有下降。性能评估表明，附加的机制使XCSF能够可靠、准确和紧凑地逼近甚至七维函数。与其他启发式函数逼近技术的性能比较表明，XCSF具有与之相当甚至更好的抗噪性能。
An important strength of learning classifier systems (LCSs) lies in the combination of genetic optimization techniques with gradient-based approximation techniques. The chosen approximation technique develops locally optimal approximations, such as accurate classification estimates, Q-value predictions, or linear function approximations. The genetic optimization technique is designed to distribute these local approximations efficiently over the problem space. Together, the two components develop a distributed, locally optimized problem solution in the form of a population of expert rules, often called classifiers. In function approximation problems, the XCSF classifier system develops a problem solution in the form of overlapping, piecewise linear approximations. This paper shows that XCSF performance on function approximation problems additively benefits from: 1) improved representations; 2) improved genetic operators; and 3) improved approximation techniques. Additionally, this paper introduces a novel closest classifier matching mechanism for the efficient compaction of XCS's final problem solution. The resulting compaction mechanism can boil the population size down by 90% on average, while decreasing prediction accuracy only marginally. Performance evaluations show that the additional mechanisms enable XCSF to reliably, accurately, and compactly approximate even seven dimensional functions. Performance comparisons with other, heuristic function approximation techniques show that XCSF yields competitive or even superior noise-robust performance.