Privately Answering Classification Queries in the Agnostic PAC Model
ALT(2019)
摘要
We revisit the problem of differentially private release of classification
queries. In this problem, the goal is to design an algorithm that can
accurately answer a sequence of classification queries based on a private
training set while ensuring differential privacy. We formally study this
problem in the agnostic PAC model and derive a new upper bound on the private
sample complexity. Our results improve over those obtained in a recent work
[BTT18] for the agnostic PAC setting. In particular, we give an improved
construction that yields a tighter upper bound on the sample complexity.
Moreover, unlike [BTT18], our accuracy guarantee does not involve any blow-up
in the approximation error associated with the given hypothesis class.
Given any hypothesis class with VC-dimension d, we show that our
construction can privately answer up to m classification queries with average
excess error α using a private sample of size ≈d/α^2 max(1, √(m) α^3/2). Using recent
results on private learning with auxiliary public data, we extend our
construction to show that one can privately answer any number of classification
queries with average excess error α using a private sample of size
≈d/α^2 max(1, √(d) α). When
α=O(1/√(d)), our private sample complexity bound
is essentially optimal.
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