Document type
Conference papers
Document subtype
Full paper
Title
Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness
Participants in the publication
Ankit Garg (Author)
Robin Kothari (Author)
Praneeth Netrapalli (Author)
Suhail Sherif (Author)
Dep. Matemática
Summary
We study the complexity of optimizing highly smooth convex functions. For a positive integer p, we want to find an approximate minimum of a convex function f, given oracle access to the function and its first p derivatives, assuming that the pth derivative of f is Lipschitz. Recently, three independent research groups (Jiang et al., PMLR 2019; Gasnikov et al., PMLR 2019; Bubeck et al., PMLR 2019) developed a new algorithm for this problem. This algorithm is known to be optimal (up to log factors) for deterministic algorithms, but known lower bounds for randomized algorithms do not match this bound. We prove a new lower bound that matches this bound (up to log factors), and holds not only for randomized algorithms, but also for quantum algorithms.
Editor(s)
M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan
Date of Acceptance
2021-10-27
Date of Publication
2021-11-09
Event
Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
Publication Identifiers
ISBN - 9781713845393
Rankings
CORE A* (2023) - 4611 - Machine learning
Download