When Does Differentially Private Learning Not Suffer in High Dimensions?

• URL: http://arxiv.org/abs/2207.00160v1
• Date: Fri, 1 Jul 2022 02:36:51 GMT
• Title: When Does Differentially Private Learning Not Suffer in High Dimensions?
• Authors: Xuechen Li, Daogao Liu, Tatsunori Hashimoto, Huseyin A. Inan, Janardhan Kulkarni, Yin Tat Lee, Abhradeep Guha Thakurta
• Abstract summary: Large pretrained models can be privately fine-tuned to achieve performance approaching that of non-private models. This seemingly contradicts known results on the model-size dependence of differentially private convex learning.
• Score: 43.833397016656704
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large pretrained models can be privately fine-tuned to achieve performance approaching that of non-private models. A common theme in these results is the surprising observation that high-dimensional models can achieve favorable privacy-utility trade-offs. This seemingly contradicts known results on the model-size dependence of differentially private convex learning and raises the following research question: When does the performance of differentially private learning not degrade with increasing model size? We identify that the magnitudes of gradients projected onto subspaces is a key factor that determines performance. To precisely characterize this for private convex learning, we introduce a condition on the objective that we term restricted Lipschitz continuity and derive improved bounds for the excess empirical and population risks that are dimension-independent under additional conditions. We empirically show that in private fine-tuning of large language models, gradients evaluated near a local optimum are mostly controlled by a few principal components. This behavior is similar to conditions under which we obtain dimension-independent bounds in convex settings. Our theoretical and empirical results together provide a possible explanation for recent successes in large-scale private fine-tuning.

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