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Deep neural networks have repeatedly been shown to be non-robust to theuncertainties of the real world, even to naturally occurring ones. A vastmajority of current approaches have focused on data-augmentation methods toexpand the range of perturbations that the classifier is exposed to whiletraining. A relatively unexplored avenue that is equally promising involvessanitizing an image as a preprocessing step, depending on the nature ofperturbation. In this paper, we propose to use control for learned models torecover from distribution shifts online. Specifically, our method applies asequence of semantic-preserving transformations to bring the shifted datacloser in distribution to the training set, as measured by the Wassersteindistance. Our approach is to 1) formulate the problem of distribution shiftrecovery as a Markov decision process, which we solve using reinforcementlearning, 2) identify a minimum condition on the data for our method to beapplied, which we check online using a binary classifier, and 3) employdimensionality reduction through orthonormal projection to aid in our estimatesof the Wasserstein distance. We provide theoretical evidence that orthonormalprojection preserves characteristics of the data at the distributional level.We apply our distribution shift recovery approach to the ImageNet-C benchmarkfor distribution shifts, demonstrating an improvement in average accuracy of upto 14.21% across a variety of state-of-the-art ImageNet classifiers. We furthershow that our method generalizes to composites of shifts from the ImageNet-Cbenchmark, achieving improvements in average accuracy of up to 9.81%. Finally,we test our method on CIFAR-100-C and report improvements of up to 8.25%.

DC4L: Distribution Shift Recovery via Data-Driven Control for Deep Learning Models