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

Finetuning 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 finetuning and its accompanying privacy concerns, differentially private (DP) finetuning of pretrained LLMs has garnered increasing attention to safeguarding the privacy of task-specific datasets. Lying at the design core of DP LLM finetuning methods is the satisfactory tradeoff between 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 finetuning 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 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 finetuning trajectory. Second, we further enhance the scalability by reducing the trainable parameters that are identified by repurposing a data-free pruning technique requiring no additional data or extra privacy budget. 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.