Unbiased Gradient Estimation with Balanced Assignments for Mixtures of Experts

• URL: http://arxiv.org/abs/2109.11817v1
• Date: Fri, 24 Sep 2021 09:02:12 GMT
• Title: Unbiased Gradient Estimation with Balanced Assignments for Mixtures of Experts
• Authors: Wouter Kool, Chris J. Maddison and Andriy Mnih
• Abstract summary: Training large-scale mixture of experts models efficiently 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. We propose two unbiased estimators based on principled assignment procedures: one that skips datapoints which exceed expert capacity, and one that samples perfectly balanced assignments.
• Score: 32.43213645631101
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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