  When applying differential privacy to sensitive data, we can often improve
performance using external information such as other sensitive data, public
data, or human priors. We propose to use the learning-augmented algorithms (or
algorithms with predictions) framework -- previously applied largely to improve
time complexity or competitive ratios -- as a powerful way of designing and
analyzing privacy-preserving methods that can take advantage of such external
information to improve utility. This idea is instantiated on the important task
of multiple quantile release, for which we derive error guarantees that scale
with a natural measure of prediction quality while (almost) recovering
state-of-the-art prediction-independent guarantees. Our analysis enjoys several
advantages, including minimal assumptions about the data, a natural way of
adding robustness, and the provision of useful surrogate losses for two novel
``meta" algorithms that learn predictions from other (potentially sensitive)
data. We conclude with experiments on challenging tasks demonstrating that
learning predictions across one or more instances can lead to large error
reductions while preserving privacy.
