On the oracle complexity of smooth strongly convex minimization

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 criter...

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Vydáno v:Journal of Complexity Ročník 68; s. 101590
Hlavní autoři: Drori, Yoel, Taylor, Adrien
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.02.2022
Elsevier
Témata:
Information-based complexity
Mathematics
Optimal methods
Optimization and Control
Oracle complexity
Strongly convex functions
Strongly convex functions
Optimal methods
Oracle complexity
Information-based complexity
ISSN:0885-064X, 1090-2708
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Popis
Shrnutí: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.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2021.101590