natural evolution strategies

Natural Evolution Strategies (NES)

Evolution strategies that use natural gradient descent to update search distribution parameters.
NES optimizes a probability distribution $p_{\psi }(\theta )$ over parameters by maximizing expected fitness:

$$\underset{\psi }{\max }{\mathbb{E}}_{\theta \sim p_{\psi }}[F(\theta )]$$

Updates use the natural gradient ${\tilde{\nabla }}_{\psi }=F^{-1}{\nabla }_{\psi }$ where $F$ is the fisher information matrix.

This ensures the algorithm takes consistent steps in distribution space rather than parameter space - a small parameter change that drastically alters the distribution is scaled appropriately.

Mathy details: https://lilianweng.github.io/posts/2019-09-05-evolution-strategies/

NES, FIM