  This paper studies \emph{differential privacy (DP)} and \emph{local
differential privacy (LDP)} in cascading bandits. Under DP, we propose an
algorithm which guarantees $\epsilon$-indistinguishability and a regret of
$\mathcal{O}((\frac{\log T}{\epsilon})^{1+\xi})$ for an arbitrarily small
$\xi$. This is a significant improvement from the previous work of
$\mathcal{O}(\frac{\log^3 T}{\epsilon})$ regret. Under
($\epsilon$,$\delta$)-LDP, we relax the $K^2$ dependence through the tradeoff
between privacy budget $\epsilon$ and error probability $\delta$, and obtain a
regret of $\mathcal{O}(\frac{K\log (1/\delta) \log T}{\epsilon^2})$, where $K$
is the size of the arm subset. This result holds for both Gaussian mechanism
and Laplace mechanism by analyses on the composition. Our results extend to
combinatorial semi-bandit. We show respective lower bounds for DP and LDP
cascading bandits. Extensive experiments corroborate our theoretic findings.
