  In this research note, we revisit the bandits with expert advice problem.
Under a restricted feedback model, we prove a lower bound of order $\sqrt{K T
\ln(N/K)}$ for the worst-case regret, where $K$ is the number of actions, $N>K$
the number of experts, and $T$ the time horizon. This matches a previously
known upper bound of the same order and improves upon the best available lower
bound of $\sqrt{K T (\ln N) / (\ln K)}$. For the standard feedback model, we
prove a new instance-based upper bound that depends on the agreement between
the experts and provides a logarithmic improvement compared to prior results.
