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Journal Articles Journal of Complexity Year : 2022

On the oracle complexity of smooth strongly convex minimization

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, thereby establishing the exact oracle complexity for this class of problems.

Dates and versions

hal-03154582 , version 1 (01-03-2021)

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Cite

Yoel Drori, Adrien Taylor. On the oracle complexity of smooth strongly convex minimization. Journal of Complexity, 2022, ⟨10.1016/j.jco.2021.101590⟩. ⟨hal-03154582⟩
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