Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator
This work addresses the challenge of robust adaptive control in systems with unknown dynamics, offering improved regret bounds for researchers and practitioners in control theory and machine learning.
The authors tackled the problem of adaptive control for the Linear Quadratic Regulator (LQR) with an unknown linear system, presenting the first provably polynomial-time algorithm that achieves high-probability sub-linear regret, and they demonstrated its flexibility by extending it to a demand forecasting problem with state constraints.
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.