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Inexact Tensor Methods with Dynamic Accuracies
Nikita Doikov · Yurii Nesterov

Tue Jul 14 01:00 PM -- 01:45 PM & Wed Jul 15 01:00 AM -- 01:45 AM (PDT) @ None #None
In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the residual in function value. We propose two dynamic strategies for choosing the inner accuracy: the first one is decreasing as $1/k^{p + 1}$, where $p \geq 1$ is the order of the method and $k$ is the iteration counter, and the second approach is using for the inner accuracy the last progress in the target objective. We show that inexact Tensor Methods with these strategies achieve the same global convergence rate as in the error-free case. For the second approach we also establish local superlinear rates (for $p \geq 2$), and propose the accelerated scheme. Lastly, we present computational results on a variety of machine learning problems for several methods and different accuracy policies.

Author Information

Nikita Doikov (Université catholique de Louvain)
Yurii Nesterov (Universite catholique de Louvain)

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