Title: Differentially Private Zeroth-Order Methods for Scalable Large Language Model Finetuning

Abstract: Fine-tuning on task-specific datasets is a widely-embraced paradigm of harnessing the powerful capability of pretrained LLMs for various downstream tasks. Due to the popularity of LLMs fine-tuning and its accompanying privacy concerns, differentially private (DP) fine-tuning of pretrained LLMs has been widely used to safeguarding the privacy of task-specific datasets. Lying at the design core of DP LLM fine-tuning methods is the satisfactory tradeoff among privacy, utility, and scalability. Most existing methods build upon the seminal work of DP-SGD. Despite pushing the scalability of DP-SGD to its limit, DP-SGD-based fine-tuning methods are unfortunately limited by the inherent inefficiency of SGD.
In this paper, we investigate the potential of DP zeroth-order methods for LLM pretraining, which avoids the scalability bottleneck of SGD by approximating the gradient with the more efficient zeroth-order gradient. Rather than treating the zeroth-order method as a drop-in replacement for SGD, this paper presents a comprehensive study both theoretically and empirically. First, we propose the stagewise DP zeroth-order method (DP-ZOSO) that dynamically schedules key hyperparameters. This design is grounded on the synergy between DP random perturbation and the gradient approximation error of the zeroth-order method, and its effect on fine-tuning trajectory.
We provide theoretical analysis for both proposed methods. We conduct extensive empirical analysis on both encoder-only masked language model and decoder-only autoregressive language model, achieving impressive results in terms of scalability and utility (compared with DPZero, DP-ZOPO improves 4.5% on SST-5, 5.5% on MNLI with RoBERTa-Large and 9.2% on CB, 3.9% on BoolQ with OPT-2.7B when $\epsilon=4$).