Robustness and Consistency in Linear Quadratic Control with Predictions

Abstract

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances consistency, which measures the competitive ratio when predictions are accurate, and robustness, which bounds the competitive ratio when predictions are inaccurate. We propose a novel $\lambda$-confident controller and prove that it maintains a competitive ratio upper bound of $1+minO({\lambda }^2ϵ)+O(1-\lambda {)}^2,O(1)+O({\lambda }^2)$ where $\lambda \in [0,1]$ is a trust parameter set based on the confidence in the predictions, and $ϵ$ is the prediction error. Further, we design a self-tuning policy that adaptively learns the trust parameter $\lambda$ with a regret that depends on $ϵ$ and the variation of perturbations and predictions.

Chenkai Yu

PhD Student in Decision, Risk, and Operations

Incentive, Information, and Computation