We propose and analyze algorithms to solve a range of learning tasks under
user-level differential privacy constraints. Rather than guaranteeing only the
privacy of individual samples, user-level DP protects a user’s entire
contribution ($m ge 1$ samples), providing more stringent but more realistic
protection against information leaks. We show that for high-dimensional mean
estimation, empirical risk minimization with smooth losses, stochastic convex
optimization, and learning hypothesis class with finite metric entropy, the
privacy cost decreases as $O(1/sqrt{m})$ as users provide more samples. In
contrast, when increasing the number of users $n$, the privacy cost decreases
at a faster $O(1/n)$ rate. We complement these results with lower bounds
showing the worst-case optimality of our algorithm for mean estimation and
stochastic convex optimization. Our algorithms rely on novel techniques for
private mean estimation in arbitrary dimension with error scaling as the
concentration radius $tau$ of the distribution rather than the entire range.
Under uniform convergence, we derive an algorithm that privately answers a
sequence of $K$ adaptively chosen queries with privacy cost proportional to
$tau$, and apply it to solve the learning tasks we consider.

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Author Of this post: <a href="http://arxiv.org/find/cs/1/au:+Levy_D/0/1/0/all/0/1">Daniel Levy</a>, <a href="http://arxiv.org/find/cs/1/au:+Sun_Z/0/1/0/all/0/1">Ziteng Sun</a>, <a href="http://arxiv.org/find/cs/1/au:+Amin_K/0/1/0/all/0/1">Kareem Amin</a>, <a href="http://arxiv.org/find/cs/1/au:+Kale_S/0/1/0/all/0/1">Satyen Kale</a>, <a href="http://arxiv.org/find/cs/1/au:+Kulesza_A/0/1/0/all/0/1">Alex Kulesza</a>, <a href="http://arxiv.org/find/cs/1/au:+Mohri_M/0/1/0/all/0/1">Mehryar Mohri</a>, <a href="http://arxiv.org/find/cs/1/au:+Suresh_A/0/1/0/all/0/1">Ananda Theertha Suresh</a>

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