Hyper-ellipsoidal conditions in XCS: rotation, linear approximation, and solution structure
Hyper-ellipsoidal conditions in XCS: rotation, linear approximation, and solution structure
复制标题
XCS 中的超椭球条件：旋转、线性近似和解结构
DOI：
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发表时间：
2006
期刊：
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通讯作者：
Stewart W. Wilson
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作者：
Martin Volker Butz;P. Lanzi;Stewart W. Wilson
学习分类器系统XCS是一个迭代的规则学习系统，它基于基于梯度的预测和规则质量估计来进化规则结构。除了分类和强化学习任务外，XCS还被用作一种有效的函数逼近器。因此，XCS学习空间划分，以实现最精确和一般的函数逼近。最近，通过用超椭球代替(1)超矩形条件和(2)用递推最小二乘法代替迭代线性逼近，改进了函数逼近方法。本文将这两种方法结合起来，评估各自的有用性。通过改变变异算子，实现了一个明确旋转椭球结构的角度变异，进一步改进了进化过程。这两个增强都提高了各种非线性函数中的XCS性能。我们还分析了演化的椭球体结构，证实了XCS根据底层函数的形状拉伸和旋转演化的椭球体。结果证实，进化方法和梯度方法的改进都可以带来显著更好的性能。
The learning classifier system XCS is an iterative rule-learning system that evolves rule structures based on gradient-based prediction and rule quality estimates. Besides classification and reinforcement learning tasks, XCS was applied as an effective function approximator. Hereby, XCS learns space partitions to enable a maximally accurate and general function approximation. Recently, the function approximation approach was improved by replacing (1) hyperrectangular conditions with hyper-ellipsoids and (2) iterative linear approximation with the recursive least squares method. This paper combines the two approaches assessing the usefulness of each. The evolutionary process is further improved by changing the mutation operator implementing an angular mutation that rotates ellipsoidal structures explicitly. Both enhancements improve XCS performance in various non-linear functions. We also analyze the evolving ellipsoidal structures confirming that XCS stretches and rotates the evolving ellipsoids according to the shape of the underlying function. The results confirm that improvements in both the evolutionary approach and the gradient approach can result in significantly better performance.