  We propose to extend the concept of private information retrieval by allowing
for distortion in the retrieval process and relaxing the perfect privacy
requirement at the same time. In particular, we study the trade-off between
download rate, distortion, and user privacy leakage, and show that in the limit
of large file sizes this trade-off can be captured via a novel
information-theoretical formulation for datasets with a known distribution.
Moreover, for scenarios where the statistics of the dataset is unknown, we
propose a new deep learning framework by leveraging a generative adversarial
network approach, which allows the user to learn efficient schemes from the
data itself. We evaluate the performance of the scheme on a synthetic Gaussian
dataset as well as on the MNIST, CIFAR-10, and LSUN datasets. For the MNIST,
CIFAR-10, and LSUN datasets, the data-driven approach significantly outperforms
a nonlearning-based scheme which combines source coding with the download of
multiple files.
