Algorithmically Effective Differentially Private Synthetic Data

We present a highly effective algorithmic approach for generating varepsilon-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset X in the hypercube [0,1]d, our algorithm generates synthetic dataset Y such that the expected 1-Wasserstein distance between the empirical measure of X and Y is O((varepsilon n)-1/d) for d≥ 2, and is O(log2(varepsilon n)(varepsilon n)-1) for d=1. The accuracy guarantee is optimal up to a constant factor for d≥ 2, and up to a logarithmic factor for d=1. Our algorithm has a fast running time of O(varepsilon dn) for all d≥ 1 and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022) for d≥ 2.