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arXiv · 1608.04544

Free Lunch for Optimisation under the Universal Distribution

Tom Everitt·Tor Lattimore·Marcus Hutter
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Abstract

Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We argue against the uniform assumption and suggest a universal prior exists for which there is a free lunch, but where no particular class of functions is favoured over another. We also prove upper and lower bounds on the size of the free lunch.

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Tom Everitt, Tor Lattimore, Marcus Hutter. 2016-08-16. Free Lunch for Optimisation under the Universal Distribution. https://doi.org/10.1109/cec.2014.6900546

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