On the Convergence of the Iterative Linear Exponential Quadratic Gaussian Algorithm to Stationary Points

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the algorithm actually minimizes and we show how the addition of a proximal term guarantees convergence to a stationary point

Primal-dual Learning for the Model-free Risk-constrained Linear Quadratic Regulator

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.Comment: To appear in the Annual Conference on Learning for Dynamics and Control (L4DC) 202