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arXiv · 2101.09740

On the oracle complexity of smooth strongly convex minimization

Yoel Drori·Adrien Taylor
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Abstract

We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of strongly-convex minimization under various inaccuracy criteria. The new bounds match the known upper bounds up to a constant factor, and when the inaccuracy of a solution is measured by its distance to the solution set, the new lower bound exactly matches the upper bound obtained by the recent Information-Theoretic Exact Method by the same authors, thereby establishing the exact oracle complexity for this class of problems.

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Yoel Drori, Adrien Taylor. 2021-01-24. On the oracle complexity of smooth strongly convex minimization. https://arxiv.org/abs/2101.09740

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