Abstract The budget allocation problem is an optimization problem arising from advertising planning. In the problem, an advertiser has limited budgets to allocate across media, and seeks to optimize the allocation such that the largest fraction of customers can be influenced. It is known that this problem admits a (1 1/e)-approximation algorithm. However, no previous studies on this problem considered adjusting the allocation adaptively based upon the effect of the past campaigns, which is a usual strategy in the real setting. Our main contribution in this paper is to analyze adaptive strategies for the budget allocation problem. We define a greedy strategy, referred to as the insensitive policy, and then give a provable performance guarantee. This result is obtained by extending the adaptive submodularity, which is a concept studied in the context of active learning and stochastic optimization, to the functions over an integer lattice.