Unbalanced minibatch Optimal Transport; applications to Domain Adaptation
This addresses computational bottlenecks in applying optimal transport to domain adaptation, offering a more robust method for practitioners, though it is incremental as it builds on existing minibatch and unbalanced transport ideas.
The paper tackles the problem of undesirable smoothing effects when using minibatch estimates for optimal transport distances in large-scale datasets, and shows that coupling minibatch strategies with unbalanced optimal transport yields significantly better results in domain adaptation tasks, competing with or surpassing recent baselines.
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.