A frequency-domain analysis of inexact gradient methods

Oran Gannot

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arXiv · 1912.13494

A frequency-domain analysis of inexact gradient methods

Oran Gannot

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Abstract

We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well as for the larger class of functions with sector-bounded gradients, under a relative error model. Proofs of the corresponding convergence rates are based on frequency-domain criteria for the stability of nonlinear systems. Applications are given to inexact versions of gradient descent and the Triple Momentum Method. To further emphasize the usefulness of frequency-domain methods, we derive improved analytic bounds for the convergence rate of Nesterov's accelerated method (in the exact setting) on strongly convex functions.

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BibTeX RIS

Oran Gannot. 2019-12-31. A frequency-domain analysis of inexact gradient methods. https://arxiv.org/abs/1912.13494

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