  Optimal transport distances have found many applications in machine learning
for their capacity to compare non-parametric probability distributions. Yet
their algorithmic complexity generally prevents their direct use on large scale
datasets. Among the possible strategies to alleviate this issue, practitioners
can rely on computing estimates of these distances over subsets of data, {\em
i.e.} minibatches. While computationally appealing, we highlight in this paper
some limits of this strategy, arguing it can lead to undesirable smoothing
effects. As an alternative, we suggest that the same minibatch strategy coupled
with unbalanced optimal transport can yield more robust behavior. We discuss
the associated theoretical properties, such as unbiased estimators, existence
of gradients and concentration bounds. Our experimental study shows that in
challenging problems associated to domain adaptation, the use of unbalanced
optimal transport leads to significantly better results, competing with or
surpassing recent baselines.
