Bayesian optimization on Riemannian manifolds for robot learning

Abstract

Fast and data efficient adaptation is a key challenge in robotics, where robots often need to generalize previously-learned skills to unforeseen settings. In this context, Bayesian optimization has gained increasing interest due to its success in efficiently optimizing parametric policies in various challenging robotics scenarios. However, improving the performance, scalability, and safety of Bayesian optimization techniques remains a central goal for robotics applications. In this talk, I will discuss how Bayesian optimization can benefit from inductive bias, which can be introduced into the algorithm via task-specific information about the geometry of the search space. Indeed, many robotic parameters belong to non-Euclidean spaces and carry such geometric information: Orientations can be viewed as elements of the unit sphere or the special orthogonal group, control gains, inertia, and manipulability ellipsoids lie in the manifold of symmetric-positive-definite matrices, and robot joint configurations belong to the torus, among others. Therefore, I will show how geometry-awareness can be brought into Bayesian optimization by exploiting Riemannian manifold theory, both in the surrogate model and in the acquisition function optimization. I will show that this improves the performance of Bayesian optimization in a variety of benchmark settings and robotics applications.

Notes

• Noémie Jaquier is a Postdoctoral researcher at Karlsruhe Institute of Technology. Personal website can be found here.