Meta-Learning Guarantees for Online Receding Horizon Learning Control
This work addresses the challenge of ensuring performance guarantees for control algorithms in dynamic, unknown environments, which is incremental as it builds on existing meta-learning and control theory.
The paper tackles the problem of providing provable regret guarantees for an online meta-learning receding horizon control algorithm in iterative control settings with unknown linear deterministic systems, general additive costs, and affine constraints. It shows that the algorithm achieves an average dynamic regret of $ ilde{O}((1+1/\sqrt{N})T^{3/4})$ with the number of iterations $N$, demonstrating improved worst regret as experience accumulates.
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.