  Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals. We demonstrate that,
ignoring computational constraints, it is possible to privately agnostically
learn any concept class using a sample size approximately logarithmic in the
cardinality of the concept class. Therefore, almost anything learnable is
learnable privately: specifically, if a concept class is learnable by a
(non-private) algorithm with polynomial sample complexity and output size, then
it can be learned privately using a polynomial number of samples. We also
present a computationally efficient private PAC learner for the class of parity
functions. Local (or randomized response) algorithms are a practical class of
private algorithms that have received extensive investigation. We provide a
precise characterization of local private learning algorithms. We show that a
concept class is learnable by a local algorithm if and only if it is learnable
in the statistical query (SQ) model. Finally, we present a separation between
the power of interactive and noninteractive local learning algorithms.
