Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging

TL;DR

This paper introduces horizon-free, anytime learning rate schedules combined with weight averaging for large language model pretraining, providing theoretical guarantees and practical effectiveness comparable to traditional cosine schedules.

Contribution

It offers the first theoretical analysis of anytime schedules for overparameterized linear regression and demonstrates their practical viability in large language model training.

Findings

Anytime schedules achieve comparable final loss to cosine decay.

Weight averaging enhances the effectiveness of horizon-free schedules.

Empirical results on 150M and 300M parameter models support the approach.

Abstract

Large language models are increasingly trained in continual or open-ended settings, where the total training horizon is not known in advance. Despite this, most existing pretraining recipes are not anytime: they rely on horizon-dependent learning rate schedules and extensive tuning under a fixed compute budget. In this work, we provide a theoretical analysis demonstrating the existence of anytime learning schedules for overparameterized linear regression, and we highlight the central role of weight averaging - also known as model merging - in achieving the minimax convergence rates of stochastic gradient descent. We show that these anytime schedules polynomially decay with time, with the decay rate determined by the source and capacity conditions of the problem. Empirically, we evaluate 150M and 300M parameter language models trained at 1-32x Chinchilla scale, comparing constant learning rates with weight averaging and $1/\sqrt{t}$ schedules with weight averaging against a well-tuned cosine schedule. Across the full training range, the anytime schedules achieve comparable final loss to cosine decay. Taken together, our results suggest that weight averaging combined with simple, horizon-free step sizes offers a practical and effective anytime alternative to cosine learning rate schedules for large language model pretraining.