Learning-Augmented Control: Adaptively Confidence Learning for Competitive MPC

TL;DR

This paper presents Learning-Augmented Control (LAC), a method that adaptively combines machine learning predictions with traditional control to ensure near-optimal performance when predictions are accurate and safety when they are not.

Contribution

The paper introduces a novel confidence learning procedure for control, providing formal guarantees and tight bounds for nonlinear and linear systems, and demonstrates its effectiveness through numerical studies.

Findings

LAC achieves near-optimal performance with accurate predictions.

LAC maintains stability and safety under adversarial errors.

Theoretical bounds are established for nonlinear and linear systems.

Abstract

We introduce Learning-Augmented Control (LAC), an approach that integrates untrusted machine learning predictions into the control of constrained, nonlinear dynamical systems. LAC is designed to achieve the "best-of-both-worlds" guarantees, i.e, near-optimal performance when predictions are accurate, and robust, safe performance when they are not. The core of our approach is a delayed confidence learning procedure that optimizes a confidence parameter online, adaptively balancing between ML and nominal predictions. We establish formal competitive ratio bounds for general nonlinear systems under standard MPC regularity assumptions. For the linear quadratic case, we derive a competitive ratio bound that is provably tight, thereby characterizing the fundamental limits of this learning-augmented approach. The effectiveness of LAC is demonstrated in numerical studies, where it maintains stability and outperforms standard methods under adversarial prediction errors.