  In the recent decades, the advance of information technology and abundant
personal data facilitate the application of algorithmic personalized pricing.
However, this leads to the growing concern of potential violation of privacy
due to adversarial attack. To address the privacy issue, this paper studies a
dynamic personalized pricing problem with \textit{unknown} nonparametric demand
models under data privacy protection. Two concepts of data privacy, which have
been widely applied in practices, are introduced: \textit{central differential
privacy (CDP)} and \textit{local differential privacy (LDP)}, which is proved
to be stronger than CDP in many cases. We develop two algorithms which make
pricing decisions and learn the unknown demand on the fly, while satisfying the
CDP and LDP gurantees respectively. In particular, for the algorithm with CDP
guarantee, the regret is proved to be at most $\tilde
O(T^{(d+2)/(d+4)}+\varepsilon^{-1}T^{d/(d+4)})$. Here, the parameter $T$
denotes the length of the time horizon, $d$ is the dimension of the
personalized information vector, and the key parameter $\varepsilon>0$ measures
the strength of privacy (smaller $\varepsilon$ indicates a stronger privacy
protection). On the other hand, for the algorithm with LDP guarantee, its
regret is proved to be at most $\tilde
O(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$, which is near-optimal as we prove a
lower bound of $\Omega(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$ for any
algorithm with LDP guarantee.
