Abstract: System identification has a long history with several well-established methods, in particular for learning linear dynamical systems from input/output data. While the asymptotic properties of these methods are well understood as the number of data points goes to infinity or the noise level tends to zero, how well their estimates in finite data regime evolve is relatively less studied. This talk will mainly focus on our analysis of the robustness of the classical Ho-Kalman algorithm and how it translates to non-asymptotic estimation error bounds as a function of number of data samples. If time permits, I will also mention another problem we study at the intersection of learning, control, and optimization: learning constraints from demonstrations as an alternative to inverse optimal control. Our experiments with several robotics problems show (local) optimality can be a very strong prior in learning from demonstrations. I will conclude the talk with some open problems and directions for future research.