Learning to optimize with convergence guarantees using nonlinear system theory

Autor:	Martin, Andrea, Furieri, Luca
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes. Classical gradient descent methods offer strong theoretical guarantees for convex problems; however, they demand meticulous hyperparameter tuning for non-convex ones. The emerging paradigm of learning to optimize (L2O) automates the discovery of algorithms with optimized performance leveraging learning models and data - yet, it lacks a theoretical framework to analyze convergence of the learned algorithms. In this paper, we fill this gap by harnessing nonlinear system theory. Specifically, we propose an unconstrained parametrization of all convergent algorithms for smooth non-convex objective functions. Notably, our framework is directly compatible with automatic differentiation tools, ensuring convergence by design while learning to optimize. Comment: Published in the IEEE Control Systems Letters
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.09389 Zobrazit plný text záznamu View this record from Arxiv