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首页> 外文期刊>Evolutionary computation >Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies
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Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies

机译：协方差矩阵的对角线加速度适应演变策略

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摘要

We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means ofadaptive diagonal decoding(dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES without inheriting its drawbacks. Technically, we introduce a diagonal matrixDthat expresses coordinate-wise variances of the sampling distribution inDCDform. The diagonal matrix can learn a rescaling of the problem in the coordinates within a linear number of function evaluations. Diagonal decoding can also exploit separability of the problem, but, crucially, does not compromise the performance on nonseparable problems. The latter is accomplished by modulating the learning rate for the diagonal matrix based on the condition number of the underlying correlation matrix. dd-CMA-ES not only combines the advantages of default and separable CMA-ES, but may achieve overadditive speedup: it improves the performance, and even the scaling, of the better of default and separable CMA-ES on classes of nonseparable test functions that reflect, arguably, a landscape feature commonly observed in practice.The article makes two further secondary contributions: we introduce two different approaches to guarantee positive definiteness of the covariance matrix with active CMA, which is valuable in particular with large population size; we revise the default parameter setting in CMA-ES, proposing accelerated settings in particular for large dimension.All our contributions can be viewed as independent improvements of CMA-ES, yet they are also complementary and can be seamlessly combined. In numerical experiments with dd-CMA-ES up to dimension 5120, we observe remarkable improvements over the original covariance matrix adaptation on functions with coordinate-wise ill-conditioning. The improvement is observed also for large population sizes up to about dimension squared.
机译：我们通过Adaptive对角线解码（DD-CMA）介绍协方差矩阵适应演化策略（CMA-ES）的加速。该对角线加速度赋予默认的CMA-ES，其具有可分离的CMA-ES的优点而不继承其缺点。从技术上讲，我们介绍了一个对角矩阵，表达了采样分布的坐标性方差Indcdform。对角线矩阵可以在线性函数评估中的线性数量内学习坐标中的问题的重构。对角线解码还可以利用问题的可分离性，但是，至关重要的是，不损害在不可密定的问题上的性能。基于基于底层相关矩阵的条件数来调制对角线矩阵的学习率来实现后者。 DD-CMA-es不仅结合了默认和可分离的CMA-es的优点，而且可以实现高度加速：它可以提高性能，甚至是缩放，默认和可分离的CMA-ES在非可分子测试功能的类上可以说，可以在实践中常见的景观特征。文章进行了两种进一步的二级贡献：我们介绍了两种不同的方法，以保证协方差与有源CMA的积极明确，特别是众多人口大小是有价值的;我们修改CMA-ES中的默认参数设置，提出了适用于大维度的加速设置。我们的贡献可以被视为CMA-es的独立改进，但它们也是互补的，可以无缝化的。在具有DD-CMA-es的数值实验中，尺寸5120，我们观察到具有坐标明智的函数的原始协方差矩阵适应性上的显着改进。对于大约尺寸平方的大型人口尺寸，也观察到改善。

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