Geometric deep learning seminar

Password to online link: 319764

Abstract: Dynamical systems are essential for modeling and analysis in many different areas, including engineering, biology, and economics. In fact, behavior observed in nature can often be modeled by dynamical systems that operate by minimizing cost or maximizing reward; this type of behavior is known as optimal control. However, a fundamental problem in applications of optimal control is to design the cost function. The reason is that the cost function must be carefully selected and tuned to the contextual environment in order to induce an appropriate control response. Inverse optimal control, also known as inverse reinforcement learning, is a method to try to overcome this issue. In the inverse problem, the task is to identify (learn) the underlying cost function with respect to which observed behavior is optimal. Here, I will present our work on inverse optimal control for discrete-time linear-quadratic systems. In particular, we formulate an estimator for the underlying (unknown) quadratic cost function from observed optimal state trajectories. This estimator is the minimizing argument to a convex optimization problem, and we prove that the estimator is statistically consistent, that is, that it converges in probability to to true underlying cost as the number of observed trajectories goes to infinity. If time be, I will also give a brief overview of how we intend to try generalize these results to more general underlying dynamics and cost functions.