  We consider the problem of finding the maximum of $\mathbb{E}_{\nu}[f(X)]$
where $\nu$ is allowed to vary over all the probability measures on a Polish
space $S$ for which $d_c(\mu,\nu)\leq \theta$, in which $d_c$ is an optimal
transport distance, $f$ a real-valued function on $S$ satisfying some
regularity, $\mu$ a ``baseline" measure and $\theta \geq 0$. Whereas some of
the derivations of the dual version of this optimization problem rely on
Fenchel duality, we impose compactness on $S$ to allow us to instead use K.
Fan's minimax theorem, which does not require vector space structure. This
allows one to avoid the use of vector spaces of measures, or dual variables
other than the Lagrange multiplier.
