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Information-theoretic lower bounds for convex optimization with erroneous oracles

2020-02-04 | |  103 |   49 |   0

Abstract 

We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle. In particular, for a given function x image.png f (x) we consider optimization when one is given access to absolute error oracles that return values in  image.pngor relative error oracles that return value in image.png. We show stark information theoretic impossibility results for minimizing convex functions and maximizing concave functions over polytopes in this model.

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