针对私有训练中的学习率调度，提出更高效的噪声生成方法。
Learning Rate Scheduling with Matrix Factorization for Private Training
- 基于矩阵分解设计适配学习率调度的噪声生成机制。
- 在CIFAR-10和IMDB上实现比传统方法更高的准确率。
- 理论可解释且内存高效，适合实际部署。
我们研究在学习率调度和相关噪声下，使用随机梯度下降进行差分隐私模型训练的问题。尽管通过矩阵分解生成的相关噪声已被证明能提升精度，但以往理论工作主要聚焦于前缀和任务——该任务假设学习率恒定，而实践中学习率调度广泛用于加速训练并改善收敛性。本文填补了这一空白，推导出单阶段与多阶段设置下广泛学习率调度的一般上下界。基于此，我们提出一种学习率感知的分解方法，在最大均方误差（MaxSE）和均值均方误差（MeanSE）指标下均优于前缀和分解。理论分析得出内存高效的构造方案，适用于实际部署；在CIFAR-10和IMDB数据集上的实验验证了该方法在私有训练中提升精度的有效性。
原文摘要 · Abstract (English)
We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.
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