Artem Agafonov (MIPT) - Inexact Tensor Methods and Their Application to Stochastic Convex Optimization

We propose general non-accelerated and accelerated tensor methods 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 firststochastic tensor method for convex optimization and obtain sufficient mini-batch sizes for eachderivative.