Robustness and Consistency in Linear Quadratic Control with Predictions

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