The Hessian Estimation Evolution Strategy
This provides an alternative covariance update mechanism for evolution strategies, though it appears incremental relative to existing CMA-ES approaches.
The authors tackled black-box optimization by developing Hessian Estimation Evolution Strategy, which updates covariance matrices by directly estimating objective function curvature, resulting in competitive performance on the BBOB/COCO testbed.
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.