  Training large-scale mixture of experts models efficiently on modern hardware
requires assigning datapoints in a batch to different experts, each with a
limited capacity. Recently proposed assignment procedures lack a probabilistic
interpretation and use biased estimators for training. As an alternative, we
propose two unbiased estimators based on principled stochastic assignment
procedures: one that skips datapoints which exceed expert capacity, and one
that samples perfectly balanced assignments using an extension of the
Gumbel-Matching distribution [29]. Both estimators are unbiased, as they
correct for the used sampling procedure. On a toy experiment, we find the
`skip'-estimator is more effective than the balanced sampling one, and both are
more robust in solving the task than biased alternatives.
