  We study private synthetic data generation for query release, where the goal
is to construct a sanitized version of a sensitive dataset, subject to
differential privacy, that approximately preserves the answers to a large
collection of statistical queries. We first present an algorithmic framework
that unifies a long line of iterative algorithms in the literature. Under this
framework, we propose two new methods. The first method, private entropy
projection (PEP), can be viewed as an advanced variant of MWEM that adaptively
reuses past query measurements to boost accuracy. Our second method, generative
networks with the exponential mechanism (GEM), circumvents computational
bottlenecks in algorithms such as MWEM and PEP by optimizing over generative
models parameterized by neural networks, which capture a rich family of
distributions while enabling fast gradient-based optimization. We demonstrate
that PEP and GEM empirically outperform existing algorithms. Furthermore, we
show that GEM nicely incorporates prior information from public data while
overcoming limitations of PMW^Pub, the existing state-of-the-art method that
also leverages public data.
