  Self-training is a standard approach to semi-supervised learning where the
learner's own predictions on unlabeled data are used as supervision during
training. In this paper, we reinterpret this label assignment process as an
optimal transportation problem between examples and classes, wherein the cost
of assigning an example to a class is mediated by the current predictions of
the classifier. This formulation facilitates a practical annealing strategy for
label assignment and allows for the inclusion of prior knowledge on class
proportions via flexible upper bound constraints. The solutions to these
assignment problems can be efficiently approximated using Sinkhorn iteration,
thus enabling their use in the inner loop of standard stochastic optimization
algorithms. We demonstrate the effectiveness of our algorithm on the CIFAR-10,
CIFAR-100, and SVHN datasets in comparison with FixMatch, a state-of-the-art
self-training algorithm. Additionally, we elucidate connections between our
proposed algorithm and existing confidence thresholded self-training approaches
in the context of homotopy methods in optimization. Our code is available at
https://github.com/stanford-futuredata/sinkhorn-label-allocation.
