We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is sufficient for each algorithm to achieve the desired accuracy. As a corollary, we propose stochastic tensor methods for convex optimization and obtain sufficient mini-batch sizes for each derivative.
@article{arxiv.2012.15636,
title = {Inexact Tensor Methods and Their Application to Stochastic Convex Optimization},
author = {Artem Agafonov and Dmitry Kamzolov and Pavel Dvurechensky and Alexander Gasnikov and Martin Takáč},
journal= {arXiv preprint arXiv:2012.15636},
year = {2022}
}