On the Convergence of Differentially-Private Fine-tuning: To Linearly Probe or to Fully Fine-tune?

Differentially private (DP) machine learning pipelines typically involve a two-phase process: non-private pre-training on a public dataset, followed by fine-tuning on private data using DP optimization techniques. In the DP setting, it has been observed that full fine-tuning may not always yield the best test accuracy, even for in-distribution data. This paper (1) analyzes the training dynamics of DP linear probing (LP) and full fine-tuning (FT), and (2) explores the phenomenon of sequential fine-tuning, starting with linear probing and transitioning to full fine-tuning (LP-FT), and its impact on test loss. We provide theoretical insights into the convergence of DP fine-tuning within an overparameterized neural network and establish a utility curve that determines the allocation of privacy budget between linear probing and full fine-tuning. The theoretical results are supported by empirical evaluations on various benchmarks and models. The findings reveal the complex nature of DP fine-tuning methods. These results contribute to a deeper understanding of DP machine learning and highlight the importance of considering the allocation of privacy budget in the fine-tuning process.