Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies
This addresses the need for stable and efficient policy adaptation in robotics, particularly for unseen task conditions, though it is incremental as it builds on existing probabilistic policy structures.
The paper tackled the problem of adapting robot motion policies to new tasks by proposing a policy optimization method that leverages the structure of Gaussian mixture models, casting it as an optimal transport problem with Wasserstein gradient flows, and showed that it outperforms baselines in task success rate and low-variance solutions.
Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies accordingly. In this context, policy optimization is the \emph{de facto} paradigm to adapt robot policies as a function of task-specific objectives. Most commonly-used motion policies carry particular structures that are often overlooked in policy optimization algorithms. We instead propose to leverage the structure of probabilistic policies by casting the policy optimization as an optimal transport problem. Specifically, we focus on robot motion policies that build on Gaussian mixture models (GMMs) and formulate the policy optimization as a Wassertein gradient flow over the GMMs space. This naturally allows us to constrain the policy updates via the $L^2$-Wasserstein distance between GMMs to enhance the stability of the policy optimization process. Furthermore, we leverage the geometry of the Bures-Wasserstein manifold to optimize the Gaussian distributions of the GMM policy via Riemannian optimization. We evaluate our approach on common robotic settings: Reaching motions, collision-avoidance behaviors, and multi-goal tasks. Our results show that our method outperforms common policy optimization baselines in terms of task success rate and low-variance solutions.