

![0_image_0.png](0_image_0.png)

The eigenvalues of the Hessian span several orders of magnitude, and the parameterization with a single predominant direction is not enough to approximate the Hessian, resulting in poor performance. The other function where R1-NES fails is the Tablet function where all but a one eigendirection has a large eigenvalue. Since the parameterization of R1-NES only allows a single direction to have a large eigenvalue, the shape of the Hessian cannot be effectively approximated.

## 5 Conclusion And Future Work

We presented a new black-box optimization algorithm R1-NES that employs a novel parameterization of the search distribution covariance matrix which allows a predominant search direction to be adjusted using the natural gradient with complexity linear in the dimensionality. The algorithm shows excellent performance in a number of high-dimensional non-separable problems that, to date, have not been solved with other parameterizations of similar complexity.

Future work will concentrate on overcoming the limitations of the algorithm
(shown in Fig 6). In particular, we intend to extend the algorithm to a) incorporate multiple search directions, and b) enable each search direction to *shrink* as well as grow.

## Acknowledgement

This research was funded in part by Swiss National Science Foundation grants 200020-122124, 200020-125038, and EU IM-CLeVeR project (\#231722).

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