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