  We describe a new approach for managing aleatoric uncertainty in the
Reinforcement Learning (RL) paradigm. Instead of selecting actions according to
a single statistic, we propose a distributional method based on the
second-order stochastic dominance (SSD) relation. This compares the inherent
dispersion of random returns induced by actions, producing a more comprehensive
and robust evaluation of the environment's uncertainty. The necessary
conditions for SSD require estimators to predict accurate second moments. To
accommodate this, we map the distributional RL problem to a Wasserstein
gradient flow, treating the distributional Bellman residual as a potential
energy functional. We propose a particle-based algorithm for which we prove
optimality and convergence. Our experiments characterize the algorithm
performance and demonstrate how uncertainty and performance are better balanced
using an \textsc{ssd} policy than with other risk measures.

Machine Learning;Machine Learning