Benefits of Learning Rate Annealing for Tuning-Robustness in Stochastic Optimization

Abstract

The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a polynomial rate, such as the widely-used cosine schedule, by demonstrating their increased robustness to initial parameter misspecification due to a coarse grid search. We present an analysis in a stochastic convex optimization setup demonstrating that the convergence rate of stochastic gradient descent with annealed schedules depends sublinearly on the multiplicative misspecification factor (i.e., the grid resolution), achieving a rate of O(^1/(2p+1)/T) where p is the degree of polynomial decay and T is the number of steps, in contrast to the O(/T) rate that arises with fixed stepsizes and exhibits a linear dependence on . Experiments confirm the increased robustness compared to tuning with a fixed stepsize, that has significant implications for the computational overhead of hyperparameter search in practical training scenarios.

Tasks

Reproductions