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It is difficult to continually update private machine learning models withnew data while maintaining privacy. Data incur increasing privacy loss -- asmeasured by differential privacy -- when they are used in repeatedcomputations. In this paper, we describe regularized empirical riskminimization algorithms that continually release models for a recent window ofdata. One version of the algorithm uses the entire data history to improve themodel for the recent window. The second version uses a sliding window ofconstant size to improve the model, ensuring more relevant models in case ofevolving data. The algorithms operate in the framework of stochastic gradientdescent. We prove that even with releasing a model at each time-step over aninfinite time horizon, the privacy cost of any data point is bounded by aconstant $\epsilon$ differential privacy, and the accuracy of the output modelsare close to optimal. Experiments on MNIST and Arxiv publications data showresults consistent with the theory.

Continual and Sliding Window Release for Private Empirical Risk Minimization