  In inverse reinforcement learning (IRL), the central objective is to infer
underlying reward functions from observed expert behaviors in a way that not
only explains the given data but also generalizes to unseen scenarios. This
ensures robustness against reward ambiguity where multiple reward functions can
equally explain the same expert behaviors. While significant efforts have been
made in addressing this issue, current methods often face challenges with
high-dimensional problems and lack a geometric foundation. This paper harnesses
the optimal transport (OT) theory to provide a fresh perspective on these
challenges. By utilizing the Wasserstein distance from OT, we establish a
geometric framework that allows for quantifying reward ambiguity and
identifying a central representation or centroid of reward functions. These
insights pave the way for robust IRL methodologies anchored in geometric
interpretations, offering a structured approach to tackle reward ambiguity in
high-dimensional settings.
