  We study incentivized exploration for the multi-armed bandit (MAB) problem
where the players receive compensation for exploring arms other than the greedy
choice and may provide biased feedback on reward. We seek to understand the
impact of this drifted reward feedback by analyzing the performance of three
instantiations of the incentivized MAB algorithm: UCB, $\varepsilon$-Greedy,
and Thompson Sampling. Our results show that they all achieve $\mathcal{O}(\log
T)$ regret and compensation under the drifted reward, and are therefore
effective in incentivizing exploration. Numerical examples are provided to
complement the theoretical analysis.
