We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and ?2 divergence uncertainty sets. We prove that our algorithms require a number of gradient evaluations independent of training set size and number of parameters, making them suitable for large-scale applications. For ?2 uncertainty sets these are the first such guarantees in the literature, and for CVaR our guarantees scale linearly in the uncertainty level rather than quadratically as in previous work. We also provide lower bounds proving the worst-case optimality of our algorithms for CVaR and a penalized version of the ?2 problem. Our primary technical contributions are novel bounds on the bias of batch robust risk estimation and the variance of a multilevel Monte Carlo gradient estimator due to Blanchet and Glynn . Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9–36 times more efficient than full-batch methods.
|Number of pages
|Advances in Neural Information Processing Systems
|Published - 2020
|34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: 6 Dec 2020 → 12 Dec 2020