How about 
*[Boosting](https://en.wikipedia.org/wiki/Boosting_(machine_learning))*<sup>1</sup>
and the *Hardcore Lemma*, as described in this paper?

> Trevisan, Luca, Madhur Tulsiani, and Salil Vadhan. "Regularity, boosting, and efficiently simulating every high-entropy distribution." *24th Annual IEEE Conference on Computational Complexity*, IEEE, 2009. ([PDF download](http://ttic.uchicago.edu/~madhurt/Papers/regularity-full.pdf).)

The *Hardcore Lemma* can be proved via LP duality:

> "if a problem is hard-on-average in a weak sense on uniformly distributed inputs, then there is a
'hardcore' subset of inputs of noticeable density
such that the problem is hard-on-average
in a much stronger sense on inputs randomly drawn from such set."

Their proof of their main result
"uses duality of linear programming (or, equivalently, the finite dimensional
Hahn-Banach Theorem) in the form of the min-max theorem for two-player zero-sum
games."

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<sup>1</sup>
"most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier."