Influence maximization is the problem of finding influential users, or nodes, in a graph so as to maximize the spread of information. It has many applications in advertising and marketing on social networks. In this paper, we study a highly generic version of influence maximization, one of optimizing influence campaigns by sequentially selecting "spread seeds" from a set of influencers, a small subset of the node population, under the hypothesis that, in a given campaign, previously activated nodes remain "persistently" active throughout and thus do not yield further rewards. This problem is in particular relevant for an important form of online marketing, known as influencer marketing, in which the marketers target a sub-population of influential people, instead of the entire base of potential buyers. Importantly, we make no assumptions on the underlying diffusion model and we work in a setting where neither a diffusion network nor historical activation data are available. We call this problem online influencer marketing with persistence (in short, OIMP). We first discuss motivating scenarios and present our general approach. We introduce an estimator on the influencers' remaining potential -- the expected number of nodes that can still be reached from a given influencer -- and justify its strength to rapidly estimate the desired value, relying on real data gathered from Twitter. We then describe a novel algorithm, GT-UCB, relying on upper confidence bounds on the remaining potential. We show that our approach leads to high-quality spreads on both simulated and real datasets, even though it makes almost no assumptions on the diffusion medium. Importantly, it is orders of magnitude faster than state-of-the-art influence maximization methods, making it possible to deal with large-scale online scenarios.