  Optimal transport distances are popular and theoretically well understood in
the context of data-driven prediction. A flurry of recent work has popularized
these distances for data-driven decision-making as well although their merits
in this context are far less well understood. This in contrast to the more
classical entropic distances which are known to enjoy optimal statistical
properties. This begs the question when, if ever, optimal transport distances
enjoy similar statistical guarantees. Optimal transport methods are shown here
to enjoy optimal statistical guarantees for decision problems faced with noisy
data.
