We present a novel black box optimization algorithm called Hessian Estimation Evolution Strategy. The algorithm updates the covariance matrix of its sampling distribution by directly estimating the curvature of the objective function. This algorithm design is targeted at twice continuously differentiable problems. For this, we extend the cumulative step-size adaptation algorithm of the CMA-ES to mirrored sampling. We demonstrate that our approach to covariance matrix adaptation is efficient by evaluation it on the BBOB/COCO testbed. We also show that the algorithm is surprisingly robust when its core assumption of a twice continuously differentiable objective function is violated. The approach yields a new evolution strategy with competitive performance, and at the same time it also offers an interesting alternative to the usual covariance matrix update mechanism.

中文翻译：

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Hessian 估计演化策略

我们提出了一种新的黑盒优化算法，称为 Hessian 估计进化策略。该算法通过直接估计目标函数的曲率来更新其采样分布的协方差矩阵。该算法设计针对两次连续可微的问题。为此，我们将 CMA-ES 的累积步长自适应算法扩展到镜像采样。我们通过在 BBOB/COCO 测试平台上对其进行评估来证明我们的协方差矩阵自适应方法是有效的。我们还表明，当违反了两次连续可微目标函数的核心假设时，该算法具有惊人的鲁棒性。该方法产生了具有竞争性能的新进化策略，