Dropout Training is Distributionally Robust Optimal

This paper shows that dropout training in generalized linear models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability 6. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. The paper makes a concrete recommendation on how to select the tuning parameter 6. The paper also provides a novel, parallelizable, unbiased multi-level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector.