We investigate various stochastic bandit problems in the presence of adversarial corruptions. A seminal work for this problem is the BARBAR~\cite{gupta2019better} algorithm, which achieves both robustness and efficiency. However, it suffers from a regret of $O(KC)$, which does not match the lower bound of $\Omega(C)$, where $K$ denotes the number of arms and $C$ denotes the corruption level. In this paper, we first improve the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ to achieve an optimal regret bound up to a logarithmic factor. We also extend BARBAT to various settings, including multi-agent bandits, graph bandits, combinatorial semi-bandits and batched bandits. Compared with the Follow-the-Regularized-Leader framework, our methods are more amenable to parallelization, making them suitable for multi-agent and batched bandit settings, and they incur lower computational costs, particularly in semi-bandit problems. Numerical experiments verify the efficiency of the proposed methods.