Data augmentation as stochastic optimization

Boris Hanin, Yi Sun

Published 2020-10-21Version 1

We present a theoretical framework recasting data augmentation as stochastic optimization for a sequence of time-varying proxy losses. This provides a unified approach to understanding techniques commonly thought of as data augmentation, including synthetic noise and label-preserving transformations, as well as more traditional ideas in stochastic optimization such as learning rate and batch size scheduling. We prove a time-varying Monro-Robbins theorem with rates of convergence which gives conditions on the learning rate and augmentation schedule under which augmented gradient descent converges. Special cases give provably good joint schedules for augmentation with additive noise, minibatch SGD, and minibatch SGD with noise.