English

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.

Keywords

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}
}