Training differentially private machine learning models requires constraining an individual's contribution to the optimization process. This is achieved by clipping the $2$-norm of their gradient at a predetermined threshold prior to averaging and batch sanitization. This selection adversely influences optimization in two opposing ways: it either exacerbates the bias due to excessive clipping at lower values, or augments sanitization noise at higher values. The choice significantly hinges on factors such as the dataset, model architecture, and even varies within the same optimization, demanding meticulous tuning usually accomplished through a grid search. In order to circumvent the privacy expenses incurred in hyperparameter tuning, we present a novel approach to dynamically optimize the clipping threshold. We treat this threshold as an additional learnable parameter, establishing a clean relationship between the threshold and the cost function. This allows us to optimize the former with gradient descent, with minimal repercussions on the overall privacy analysis. Our method is thoroughly assessed against alternative fixed and adaptive strategies across diverse datasets, tasks, model dimensions, and privacy levels. Our results demonstrate its comparable or superior performance in all evaluated scenarios, given the same privacy requirements.

通过将剪切阈值视为可学习参数，我们提出了一种新的方法来动态优化差分隐私机器学习模型的训练过程，从而在不牺牲整体隐私分析的情况下，在各种评估场景中展现出与传统方法相媲美甚至更好的性能。

差分隐私学习中的在线敏感性优化