Before revision:  Combining CO with the oracle we designed for the offline problem, our online learning algorithm tackles the budget allocation, parameter learning, and reward maximization challenges simultaneously. We prove that our online learning algorithm achieves a scaled regret comparable to that of the  UCB-based algorithms for IM semi-bandits.
After revision:  Combining CO with the oracle we designed for the offline problem, our online learning algorithm tackles the budget allocation, parameter learning, and reward maximization . We show that for IM semi-bandits, our TS-based algorithm achieves a scaled regret comparable to that of the UCB-based algorithms for IM semi-bandits.