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arXiv · 2012.15636

Inexact Tensor Methods and Their Application to Stochastic Convex Optimization

Artem Agafonov·Dmitry Kamzolov·Pavel Dvurechensky·Alexander Gasnikov·Martin Takáč
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Abstract

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.

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Artem Agafonov, Dmitry Kamzolov, Pavel Dvurechensky, Alexander Gasnikov, Martin Takáč. 2020-12-31. Inexact Tensor Methods and Their Application to Stochastic Convex Optimization. https://arxiv.org/abs/2012.15636

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