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Robots often rely on a repertoire of previously-learned motion policies forperforming tasks of diverse complexities. When facing unseen task conditions orwhen new task requirements arise, robots must adapt their motion policiesaccordingly. 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 oftenoverlooked in policy optimization algorithms. We instead propose to leveragethe structure of probabilistic policies by casting the policy optimization asan optimal transport problem. Specifically, we focus on robot motion policiesthat build on Gaussian mixture models (GMMs) and formulate the policyoptimization as a Wassertein gradient flow over the GMMs space. This naturallyallows us to constrain the policy updates via the $L^2$-Wasserstein distancebetween GMMs to enhance the stability of the policy optimization process.Furthermore, we leverage the geometry of the Bures-Wasserstein manifold tooptimize the Gaussian distributions of the GMM policy via Riemannianoptimization. We evaluate our approach on common robotic settings: Reachingmotions, collision-avoidance behaviors, and multi-goal tasks. Our results showthat our method outperforms common policy optimization baselines in terms oftask success rate and low-variance solutions.

Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies