On the oracle complexity of smooth strongly convex minimization
Optimization and Control
2021-06-16 v2
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.
Cite
@article{arxiv.2101.09740,
title = {On the oracle complexity of smooth strongly convex minimization},
author = {Yoel Drori and Adrien Taylor},
journal= {arXiv preprint arXiv:2101.09740},
year = {2021}
}