Improvement of sep-CMA-ES for Optimization of High-Dimensional Functions with Low Effective Dimensionality
Improvement of sep-CMA-ES for Optimization of High-Dimensional Functions with Low Effective Dimensionality
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DOI：
10.1109/ssci51031.2022.10022244
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Teppei Yamaguchi;Kento Uchida;Shinichi Shirakawa
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文献类型：
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作者：
Teppei Yamaguchi;Kento Uchida;Shinichi Shirakawa
高维黑箱优化问题通常涉及一种被称为低有效维度（LED）的特性，其中设计变量包含许多几乎不影响目标函数值的冗余元素。协方差矩阵自适应进化策略（CMA - ES）在具有低有效维度的目标函数上性能会下降，因为冗余维度会导致适度的超参数设置，并减慢步长的自适应。在本研究中，我们关注可分离的CMA - ES（sep - CMA - ES），它是CMA - ES的一种变体，将协方差矩阵限制为对角矩阵，并提出一种方法，利用均值向量更新和秩 - μ更新中的逐元素信噪比来估计每个维度的有效性。利用估计的有效性，我们针对低有效维度构建了两种对策，包括超参数的自适应以及累积步长自适应和两点步长自适应中更新规则的细化，从而提出了sep - CMA - ES - LED。我们通过实验表明，与原始的sep - CMA - ES相比，sep - CMA - ES - LED在几个具有低有效维度的基准函数上表现良好。
High-dimensional black-box optimization problems often involve a property referred to as low effective dimensionality (LED), in which design variables contain many redundant elements that scarcely affect the objective function value. The covariance matrix adaptation evolution strategy (CMA-ES) suffers a performance deterioration on objective functions with LED because the redundant dimensions lead to modest hyperparameter settings and slow down the adaptation of the step-size. In this study, we focus on the separable CMA-ES (sep-CMA-ES), a variant of CMA-ES that restricts the covariance matrix to be diagonal, and propose a method to estimate the effectiveness of each dimension using the element-wise signal-to-noise ratios in the mean vector update and rank-µ update. Using the estimated effectiveness, we construct two countermeasures for LED, including an adaptation of hyperparameters and a refinement of the update rule in the cumulative step-size adaptation and two-point step-size adaptation, proposing sep-CMA-ES-LED. We experimentally showed that sep-CMA-ES-LED performed well on several benchmark functions with LED compared to the original sep-CMA-ES.