Abstract:We consider the question of adaptive data analysis within the framework of convex optimization. We ask how many samples are needed in order to compute ε-accurate estimates of O(1/ε 2 ) gradients queried by gradient descent, and we provide two intermediate answers to this question.First, we show that for a general analyst (not necessarily gradient descent) Ω(1/ε 3 ) samples are required. This rules out the possibility of a foolproof mechanism. Our construction builds upon a new lower bound (that may be of inter… Show more
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