Learning ensembles by bagging can substantially improve the generalization performance of low-bias high-variance estimators, including those evolved by Genetic Programming (GP). Yet, the best way to learn ensembles in GP remains to be determined. This work attempts to fill the gap between existing GP ensemble learning algorithms, which are often either simple but expensive, or efficient but complex. We propose a new algorithm that is both simple and efficient, named Simple Simultaneous Ensemble Genetic Programming (2SEGP). 2SEGP is obtained by relatively minor modifications to fitness evaluation and selection of a classic GP algorithm, and its only drawback is an (arguably small) increase of the fitness evaluation cost from the classic $\mathcal{O}(n \ell)$ to $\mathcal{O}(n(\ell + \beta))$, with $n$ the number of observations and $\ell$/$\beta$ the estimator/ensemble size. Experimental comparisons on real-world datasets between supervised classification and regression show that, despite its simplicity, 2SEGP fares very well against state-of-the-art (ensemble and not) GP algorithms. We further provide insights into what matters in 2SEGP by (i) scaling $\beta$, (ii) ablating the proposed selection method, (iii) observing the evolvability induced by traditional subtree variation.

中文翻译：

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遗传编程中的简单同时集成学习

通过装袋学习集成可以显着提高低偏差高方差估计器的泛化性能，包括那些由遗传编程 (GP) 进化而来的估计器。然而，在 GP 中学习合奏的最佳方式仍有待确定。这项工作试图填补现有 GP 集成学习算法之间的空白，这些算法通常要么简单但昂贵，要么高效但复杂。我们提出了一种既简单又高效的新算法，称为简单同时集成遗传编程（2SEGP）。2SEGP 是通过对经典 GP 算法的适应度评估和选择进行相对较小的修改而获得的，它唯一的缺点是适应度评估成本从经典的 $\mathcal{O}(n\ell)$ 增加（可以说很小）到$\mathcal{O}(n(\ell + \beta))$, $n$ 是观察的数量，$\ell$/$\beta$ 是估计器/集合的大小。监督分类和回归之间对真实世界数据集的实验比较表明，尽管 2SEGP 很简单，但与最先进的（集成和非集成）GP 算法相比，它表现得非常好。我们通过 (i) 缩放 $\beta$，(ii) 消除所提出的选择方法，(iii) 观察由传统子树变异引起的可进化性，进一步深入了解 2SEGP 中的重要性。