On Adaptivity Gaps of Influence Maximization under the Independent Cascade Model with Full Adoption Feedback

Abstract: In this paper, we study the adaptivity gap of the influence maximization problem under independent cascade model when full-adoption feedback is available. Our main results are to derive upper bounds on several families of well-studied influence graphs, including in-arborescences, out-arborescences and bipartite graphs. Especially, we prove that the adaptivity gap for the in-arborescence is between $[\frac{e}{e-1}, \frac{2e}{e - 1}]$ and for the out-arborescence, the gap is between $[\frac{e}{e-1}, 2]$. These are the first constant upper bounds in the full-adoption feedback model. We provide several novel ideas to tackle with correlated feedback appearing in the adaptive stochastic optimization, which we believe to be of independent interests.