LMO-DP: Optimizing the Randomization Mechanism for Differentially Private Fine-Tuning (Large) Language Models

Differentially Private Stochastic Gradient Descent (DP-SGD) and its variants have been proposed to ensure rigorous privacy for fine-tuning large-scale pre-trained language models. However, they rely heavily on the Gaussian mechanism, which may overly perturb the gradients and degrade the accuracy, especially in stronger privacy regimes (e.g., the privacy budget ε < 3). To address such limitations, we propose a novel Language Model-based Optimal Differential Privacy (LMO-DP) mechanism, which takes the first step to enable the tight composition of accurately fine-tuning (large) language models with a sub-optimal DP mechanism, even in strong privacy regimes (e.g., 0.1≤ ε<3). Furthermore, we propose a novel offline optimal noise search method to efficiently derive the sub-optimal DP that significantly reduces the noise magnitude. For instance, fine-tuning RoBERTa-large (with 300M parameters) on the SST-2 dataset can achieve an accuracy of 92.20% (given ε=0.3, δ=10-10) by drastically outperforming the Gaussian mechanism (e.g., ~ 50% for small ε and δ). We also draw similar findings on the text generation tasks on GPT-2. Finally, to our best knowledge, LMO-DP is also the first solution to accurately fine-tune Llama-2 with strong differential privacy guarantees. The code will be released soon and available upon request.