WIAS Preprint No. 2818, (2021)

Inexact tensor methods and their application to stochastic convex optimization


  • Agafonov, Artem
  • Kamzolov, Dmitry
  • Dvurechensky, Pavel
    ORCID: 0000-0003-1201-2343
  • Gasnikov, Alexander

2020 Mathematics Subject Classification

  • 90C30 90C25 68Q25


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

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