Inexact Tensor Methods with Dynamic Accuracies

Nikita Doikov () and Yurii Nesterov ()
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Nikita Doikov: Université catholique de Louvain, ICTEAM
Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium

No 3309, LIDAM Reprints CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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/kp+1, where p ≥ 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 ≥ 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.

Pages: 10
Date: 2024-01-01
Note: In: Proceedings of the 37th International Conference on Machine Learning, PMLR, 2020, vol. 119, p. 2577-2586
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