Information-theoretic lower bounds for convex optimization with erroneous oracles

Part of Advances in Neural Information Processing Systems 28 (NIPS 2015)

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Yaron Singer, Jan Vondrak


We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle. In particular, for a given function $x \to f(x)$ we consider optimization when one is given access to absolute error oracles that return values in [f(x) - \epsilon,f(x)+\epsilon] or relative error oracles that return value in [(1+\epsilon)f(x), (1 +\epsilon)f (x)], for some \epsilon larger than 0. We show stark information theoretic impossibility results for minimizing convex functions and maximizing concave functions over polytopes in this model.