Talk:Natural evolution strategy

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I recently read the paper listed below (information is provided in bibtex form). Specifically the problem reduces significantly when one is using a class of exponential distributions. It says one alternative to premultiplying by the inverse of the Fisher information matrix is to use an update rule in "natural coordinates." The natural coordinates set the Fisher information matrix to the identity matrix. Basically natural coordinates have zero mean and unit variance. They are introduced symbolically, allowing one to take the derivative with respect to them as they vanish. The reparameterized problem looks like
${\displaystyle \mu \leftarrow \mu +A\,\delta ,}$
and
${\displaystyle A\leftarrow A\,\exp(M),}$
where ${\displaystyle \Sigma =A\,A^{\intercal }}$. Then one obtains the update rules by taking the symbolic derivative with respect to ${\displaystyle \delta }$ and ${\displaystyle M}$ about zero and the zero matrix. Thus, if my understanding is correct, this results in the Fisher information matrix equaling the identity matrix.

@INPROCEEDINGS{Glasmachers2010,

 author = {Glasmachers, Tobias and Schaul, Tom and Sun, Yi and Wierstra, Daan and Schmidhuber, J\"{u}rgen},
 title = {Exponential natural evolution strategies},
 booktitle = {Proceedings of the 12th annual conference on Genetic and evolutionary computation},
 year = {2010},
 series = {GECCO '10},
 pages = {393--400},
 address = {New York, NY, USA},
 publisher = {ACM},
 acmid = {1830557},
 doi = {10.1145/1830483.1830557},
 isbn = {978-1-4503-0072-8},
 keywords = {black box optimization, evolution strategies, natural gradient, unconstrained optimization},
 location = {Portland, Oregon, USA},
 numpages = {8},
 owner = {Michael},
 timestamp = {2012.02.16},
 url = {http://doi.acm.org/10.1145/1830483.1830557}

}

The article relies heavily on "natural gradient", however it is not described anywhere in Wikipedia. The linked page doesn't mention it at all. — Preceding unsigned comment added by 193.156.79.200 (talk) 14:15, 10 February 2016 (UTC)Reply