Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees
Optimization and Control
2018-06-13 v2
Abstract
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov function (with given states), and only relies on solving a small-sized semidefinite program. Our approach combines the advantages of performance estimation problems (PEP, due to Drori & Teboulle (2014)) and integral quadratic constraints (IQC, due to Lessard et al. (2016)), and relies on convex interpolation (due to Taylor et al. (2017c;b)).
Cite
@article{arxiv.1803.06073,
title = {Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees},
author = {Adrien Taylor and Bryan Van Scoy and Laurent Lessard},
journal= {arXiv preprint arXiv:1803.06073},
year = {2018}
}
Comments
to appear in ICML'18