  In this work, we study the problem of answering $k$ queries with $(\epsilon,
\delta)$-differential privacy, where each query has sensitivity one. We give an
algorithm for this task that achieves an expected $\ell_\infty$ error bound of
$O(\frac{1}{\epsilon}\sqrt{k \log \frac{1}{\delta}})$, which is known to be
tight (Steinke and Ullman, 2016).
  A very recent work by Dagan and Kur (2020) provides a similar result, albeit
via a completely different approach. One difference between our work and theirs
is that our guarantee holds even when $\delta < 2^{-\Omega(k/(\log k)^8)}$
whereas theirs does not apply in this case. On the other hand, the algorithm of
Dagan and Kur has a remarkable advantage that the $\ell_{\infty}$ error bound
of $O(\frac{1}{\epsilon}\sqrt{k \log \frac{1}{\delta}})$ holds not only in
expectation but always (i.e., with probability one) while we can only get a
high probability (or expected) guarantee on the error.
