  In many applications, the labeled data at the learner's disposal is subject
to privacy constraints and is relatively limited. To derive a more accurate
predictor for the target domain, it is often beneficial to leverage publicly
available labeled data from an alternative domain, somewhat close to the target
domain. This is the modern problem of supervised domain adaptation from a
public source to a private target domain. We present two $(\epsilon,
\delta)$-differentially private adaptation algorithms for supervised
adaptation, for which we make use of a general optimization problem, recently
shown to benefit from favorable theoretical learning guarantees. Our first
algorithm is designed for regression with linear predictors and shown to solve
a convex optimization problem. Our second algorithm is a more general solution
for loss functions that may be non-convex but Lipschitz and smooth. While our
main objective is a theoretical analysis, we also report the results of several
experiments first demonstrating that the non-private versions of our algorithms
outperform adaptation baselines and next showing that, for larger values of the
target sample size or $\epsilon$, the performance of our private algorithms
remains close to that of the non-private formulation.
