Inexact tensor methods and their application to stochastic convex optimization

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.

Keywords

High-order methods, tensor methods, convex optimization, inexact derivatives, stochastic optimization

URI

https://oa.tib.eu/renate/handle/123456789/9536
https://doi.org/10.34657/8574

Citation

Agafonov, A., Kamzolov, D., Dvurechensky, P., & Gasnikov, A. (2021). Inexact tensor methods and their application to stochastic convex optimization (Vol. 2818). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2818

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Mathematik

License

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