Computing Exact Guarantees for Differential Privacy
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Quantification of the privacy loss associated with a randomised algorithm has become an active area of research and (ε,δ)-differential privacy has arisen as the standard measure of it. We propose a numerical method for evaluating the parameters of differential privacy for algorithms with continuous one dimensional output. In this way the parameters ε and δ can be evaluated, for example, for the subsampled multidimensional Gaussian mechanism which is also the underlying mechanism of differentially private stochastic gradient descent. The proposed method is based on a numerical approximation of an integral formula which gives the exact (ε,δ)-values. The approximation is carried out by discretising the integral and by evaluating discrete convolutions using a fast Fourier transform algorithm. We give theoretical error bounds which show the convergence of the approximation and guarantee its accuracy to an arbitrary degree. Experimental comparisons with state-of-the-art techniques illustrate the efficacy of the method. Python code for the proposed method can be found in Github (https://github.com/DPBayes/PLD-Accountant/).
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