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 $1 + \min{O(\lambda^2 \epsilon) + O(1 - \lambda)^2, O(1) + O(\lambda^2)}$ where $\lambda \in [0, 1]$ is a trust parameter set based on the confidence in the predictions, and $\epsilon$ is the prediction error. Further, we design a self-tuning policy that adaptively learns the trust parameter $\lambda$ with a regret that depends on $\epsilon$ and the variation of perturbations and predictions.
