Differentiable and Bilevel Optimization for Control in Robotics (PhD Defense)

PhD Defense, Benoit Landry, 03/12/2021 Title: Differentiable and Bilevel Optimization for Control in Robotics Abstract: Progress in numerical optimization is at the core of most modern advances in control for robotics. By now, almost every single class of mathematical program - quadratic, semidefinite, mixed integer - has found its way into cutting edge planning and control algorithms. Over the last few years, a certain class of optimization problems called bilevel optimization, where two mathematical programs are nested into one another, have gained renewed attention thanks to newfound abilities to solve these problems efficiently. In this talk, I will give an overview of our work on bilevel optimization, and our progress on leveraging this class of problems to move us closer to computationally tractable control of nonlinear systems. Specifically, I will demonstrate how it is possible to design novel solution methods that utilize advances in automatic differentiation while retaining the benefits of state of the art constrained nonlinear optimization solvers. I will also demonstrate how particularly challenging problems of nonlinear control such as planning through contact, adversarial learning of value functions, and Lyapunov synthesis can all surprisingly be tackled by explicitly addressing them as bilevel optimization problems.