Online Influence Maximization under Linear Threshold Model

TL;DR

This paper introduces a novel online influence maximization algorithm for the linear threshold model, providing the first theoretical regret bounds and addressing challenges of node-level feedback in social networks.

Contribution

It develops the LT-LinUCB algorithm with proven regret bounds and proposes a simpler, model-independent method OIM-ETC with competitive regret.

Findings

First regret bound for OIM under LT model.

LT-LinUCB algorithm consistent with node-level feedback.

OIM-ETC algorithm with T^{2/3} regret bound.

Abstract

Online influence maximization (OIM) is a popular problem in social networks to learn influence propagation model parameters and maximize the influence spread at the same time. Most previous studies focus on the independent cascade (IC) model under the edge-level feedback. In this paper, we address OIM in the linear threshold (LT) model. Because node activations in the LT model are due to the aggregated effect of all active neighbors, it is more natural to model OIM with the node-level feedback. And this brings new challenge in online learning since we only observe aggregated effect from groups of nodes and the groups are also random. Based on the linear structure in node activations, we incorporate ideas from linear bandits and design an algorithm LT-LinUCB that is consistent with the observed feedback. By proving group observation modulated (GOM) bounded smoothness property, a novel result of the influence difference in terms of the random observations, we provide a regret of order $\tilde{O}(\mathrm{poly}(m)\sqrt{T})$, where $m$ is the number of edges and $T$ is the number of rounds. This is the first theoretical result in such order for OIM under the LT model. In the end, we also provide an algorithm OIM-ETC with regret bound $O(\mathrm{poly}(m)\ T^{2/3})$, which is model-independent, simple and has less requirement on online feedback and offline computation.