Never Go Full Batch (in Stochastic Convex Optimization)

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

Paper

Bibtek download is not available in the pre-proceeding


Authors

Idan Amir, Yair Carmon, Tomer Koren, Roi Livni

Abstract

We study the generalization performance of $\text{\emph{full-batch}}$ optimization algorithms for stochastic convex optimization: these are first-order methods that only access the exact gradient of the empirical risk (rather than gradients with respect to individual data points), that include a wide range of algorithms such as gradient descent, mirror descent, and their regularized and/or accelerated variants. We provide a new separation result showing that, while algorithms such as stochastic gradient descent can generalize and optimize the population risk to within $\epsilon$ after $O(1/\epsilon^2)$ iterations, full-batch methods either need at least $\Omega(1/\epsilon^4)$ iterations or exhibit a dimension-dependent sample complexity.