  In this paper, we provide lower bounds for Differentially Private (DP) Online
Learning algorithms. Our result shows that, for a broad class of
$(\varepsilon,\delta)$-DP online algorithms, for number of rounds $T$ such that
$\log T\leq O(1 / \delta)$, the expected number of mistakes incurred by the
algorithm grows as $\Omega(\log \frac{T}{\delta})$. This matches the upper
bound obtained by Golowich and Livni (2021) and is in contrast to non-private
online learning where the number of mistakes is independent of $T$. To the best
of our knowledge, our work is the first result towards settling lower bounds
for DP-Online learning and partially addresses the open question in Sanyal and
Ramponi (2022).
