We show that GWG exhibits strong convergence guarantees.

In this paper, we investigate how to extend the MFLD framework to convex optimization problems over signed measures.

Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities.

Despite the widespread success of Transformers across various domains, their optimization guarantees in large-scale model settings are not well-understood.

Below, we proceed to describe our contributions in greater detail. Our framework builds upon the seminal work of Jordan et al. [1998], which introduced the celebrated

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.