Meta-Learning Guarantees for Online Receding Horizon Learning Control

TL;DR

This paper establishes regret guarantees for an online meta-learning receding horizon control algorithm applied to unknown linear systems, demonstrating improved learning performance over multiple iterations.

Contribution

It provides the first provable regret bounds for meta-learning-based receding horizon control in iterative, unknown linear systems with constraints.

Findings

Achieves sub-linear regret with increasing iterations.

Regret bound improves as the number of iterations grows.

Guarantees rate of learning improvement over time.

Abstract

In this paper we provide provable regret guarantees for an online meta-learning receding horizon control algorithm in an iterative control setting. We consider the setting where, in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and there are affine control input constraints. By analysing conditions under which sub-linear regret is achievable, we prove that the meta-learning online receding horizon controller achieves an average of the dynamic regret for the controller cost that is $\tilde{O}((1+1/\sqrt{N})T^{3/4})$ with the number of iterations $N$. Thus, we show that the worst regret for learning within an iteration improves with experience of more iterations, with guarantee on rate of improvement.