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

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

12 Mar 2025arXiv:2503.09411archive 2025-07-28

Amit Attia, Tomer Koren

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 ρ (i.e., the grid resolution), achieving a rate of O(ρ^(1/(2p+1))/√(T)) where p is the degree of polynomial decay and T is the number of steps, in contrast to the O(ρ/√(T)) rate that arises with fixed stepsizes and exhibits a linear dependence on ρ. 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.

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