Primal-dual Learning for the Model-free Risk-constrained Linear Quadratic Regulator
This work is significant for control engineers and practitioners who need to design risk-aware controllers for linear systems where the exact dynamical model is unknown, offering a data-driven solution.
This paper addresses the challenge of risk-aware control in linear systems without requiring an exact dynamical model. It formulates the problem as a discrete-time infinite-horizon LQR with a state predictive variance constraint and proposes a model-free primal-dual learning framework to optimize the controller using only data.
Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it as a discrete-time infinite-horizon LQR problem with a state predictive variance constraint. To solve it, we parameterize the policy with a feedback gain pair and leverage primal-dual methods to optimize it by solely using data. We first study the optimization landscape of the Lagrangian function and establish the strong duality in spite of its non-convex nature. Alongside, we find that the Lagrangian function enjoys an important local gradient dominance property, which is then exploited to develop a convergent random search algorithm to learn the dual function. Furthermore, we propose a primal-dual algorithm with global convergence to learn the optimal policy-multiplier pair. Finally, we validate our results via simulations.