# The Hessian Estimation Evolution Strategy

Source: [The Hessian Estimation Evolution Strategy](<https://www.sota2.com/research/paper/68fa67b81e209131cea18190>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T22:21:05.859Z

Authors: Tobias Glasmachers, Oswin Krause

Published: 2020-03-30T08:01:16.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2003.13256>)

[PDF](<https://arxiv.org/pdf/2003.13256.pdf>)