Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees
This work addresses safe and efficient control for systems with unknown dynamics, offering a solution with theoretical guarantees, though it is incremental in combining existing methods for safety and regret.
The paper tackles the problem of adaptive control for unknown linear systems with quadratic costs and safety constraints, proposing a polynomial-time algorithm that ensures constraint satisfaction and achieves a regret bound of ̃O(T^{2/3}) compared to the optimal safe controller.
We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration, performance, and computation. To address these challenges, we propose a polynomial-time algorithm that guarantees feasibility and constraint satisfaction with high probability under proper conditions. Our algorithm is implemented on a single trajectory and does not require system restarts. Further, we analyze the regret of our learning algorithm compared to the optimal safe linear controller with known model information. The proposed algorithm can achieve a $\tilde O(T^{2/3})$ regret, where $T$ is the number of stages and $\tilde O(\cdot)$ absorbs some logarithmic terms of $T$.