Scaling laws have emerged as important components of large language model (LLM) training as they can predict performance gains through scale, and provide guidance on important hyper-parameter choices that would otherwise be expensive. LLMs also rely on large, high-quality training datasets, like those sourced from (sometimes sensitive) user data. Training models on this sensitive user data requires careful privacy protections like differential privacy (DP). However, the dynamics of DP training are significantly different, and consequently their scaling laws are not yet fully understood. In this work, we establish scaling laws that accurately model the intricacies of DP LLM training, providing a complete picture of the compute-privacy-utility and the optimal training configurations in many settings.

This paper systematically studies the privacy / utility / compute trade-off for training language models with DP-SGD. Our experiments and analysis allow training compute-optimal language models by efficiently allocating the compute budget among the batch size, model size, and number of iterations. The results cover an exhaustive range of reasonable privacy budgets and dataset sizes, both of which significantly influence the optimal compute allocation and achievable loss.