WIAS Preprint No. 2818, (2021)
Inexact tensor methods and their application to stochastic convex optimization
Authors
- Agafonov, Artem
- Kamzolov, Dmitry
- Dvurechensky, Pavel
ORCID: 0000-0003-1201-2343 - Gasnikov, Alexander
2020 Mathematics Subject Classification
- 90C30 90C25 68Q25
Keywords
- High-order methods, tensor methods, convex optimization, inexact derivatives, stochastic optimization
DOI
Abstract
We propose a general non-accelerated tensor method under inexact information on higher- order derivatives, analyze its convergence rate, and provide sufficient conditions for this method to have similar complexity as the exact tensor method. As a corollary, we propose the first stochastic tensor method for convex optimization and obtain sufficient mini-batch sizes for each derivative.
Appeared in
- Optim. Methods Softw., 39 (2024), pp. 42--83 (published online in Nov. 2023), DOI 10.1080/10556788.2023.2261604 .
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