Bayesian Optimization Meets Riemannian Manifolds in Robot Learning
This work addresses a domain-specific bottleneck in robotics by enhancing BO efficiency for non-Euclidean parameter spaces, though it is incremental as it builds on existing BO frameworks.
The paper tackled the problem of Bayesian optimization (BO) performance degradation in high-dimensional parameter spaces by incorporating Riemannian manifold theory to handle non-Euclidean geometries common in robotics, resulting in improved optimization for tasks like robot manipulation with orientation and impedance parameters.
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromised when the parameter space is high-dimensional. A way to tackle this problem is to introduce domain knowledge into the BO framework. We propose to exploit the geometry of non-Euclidean parameter spaces, which often arise in robotics (e.g. orientation, stiffness matrix). Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on the manifold as an unconstrained problem. We test our approach in several benchmark artificial landscapes and using a 7-DOF simulated robot to learn orientation and impedance parameters for manipulation skills.