Electrical Engineering and Systems Science > Systems and Control
[Submitted on 14 Mar 2024 (v1), last revised 3 Jun 2024 (this version, v2)]
Title:Learning to optimize with convergence guarantees using nonlinear system theory
View PDF HTML (experimental)Abstract: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.
Submission history
From: Luca Furieri [view email][v1] Thu, 14 Mar 2024 13:40:26 UTC (199 KB)
[v2] Mon, 3 Jun 2024 09:10:27 UTC (277 KB)
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