  As intelligent agents become autonomous over longer periods of time, they may
eventually become lifelong counterparts to specific people. If so, it may be
common for a user to want the agent to master a task temporarily but later on
to forget the task due to privacy concerns. However enabling an agent to
\emph{forget privately} what the user specified without degrading the rest of
the learned knowledge is a challenging problem. With the aim of addressing this
challenge, this paper formalizes this continual learning and private unlearning
(CLPU) problem. The paper further introduces a straightforward but exactly
private solution, CLPU-DER++, as the first step towards solving the CLPU
problem, along with a set of carefully designed benchmark problems to evaluate
the effectiveness of the proposed solution. The code is available at
https://github.com/Cranial-XIX/Continual-Learning-Private-Unlearning.
