Tipo
Artigos em Conferência
Tipo de Documento
Artigo Completo
Título
Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness
Participantes na publicação
Ankit Garg (Author)
Robin Kothari (Author)
Praneeth Netrapalli (Author)
Suhail Sherif (Author)
Dep. Matemática
Resumo
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
M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan
Data de Aceitação
2021-10-27
Data de Publicação
2021-11-09
Evento
Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
Identificadores da Publicação
ISBN - 9781713845393
Identificadores de Qualidade
CORE A* (2023) - 4611 - Machine learning
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