Today's top advertisers typically manage hundreds of campaigns simultaneously and consistently launch new ones throughout the year. A crucial challenge for marketing managers is determining the optimal allocation of limited budgets across various ad lines in each campaign to maximize cumulative returns, especially given the huge uncertainty in return outcomes. In this paper, we propose to formulate budget allocation as a multi-task combinatorial bandit problem and introduce a novel online budget allocation system. The proposed system: i) integrates a Bayesian hierarchical model to intelligently utilize the metadata of campaigns and ad lines and budget size, ensuring efficient information sharing; ii) provides the flexibility to incorporate diverse modeling techniques such as Linear Regression, Gaussian Processes, and Neural Networks, catering to diverse environmental complexities; and iii) employs the Thompson sampling technique to strike a balance between exploration and exploitation. Through extensive empirical evaluations with both synthetic data and real-world data from Amazon campaigns, our system demonstrates robustness and adaptability, effectively maximizing the overall cumulative returns. A Python implementation of the proposed procedure is available at https://anonymous.4open.science/r/MCMAB.