Online Influence Maximization: Concept and Algorithm
Jianxiong Guo
TL;DR
This survey surveys Online Influence Maximization (Online IM), framing it as an online learning problem that learns unknown diffusion parameters $p_{uv}$ in diffusion models like the Independent Cascade and Linear Threshold. It establishes the Combinatorial Multi-Armed Bandit with Probabilistically Triggered Arms (CMAB-T) as the foundational framework, and reviews how edge-level, node-level, and other feedback models drive online algorithms and regret guarantees, including TPM-bounded analyses that yield near-optimal rates. The article summarizes traditional and ML-based Offline IM algorithms used as oracles, explains their integration into Online IM, and surveys a wide range of algorithms (CUCB, CTS, GP-UCB, GT-UCB, GLM-LinUCB, OCIM variants) across settings such as topic-, budget-, and competitive-aware IM, with attention to practical challenges like delayed feedback and real-data applicability. It further discusses innovative modeling, real-world variants, and future directions, highlighting the need for data-driven, model-agnostic online frameworks and the extension of CMAB theory to broader diffusion models and feedback realities. The work serves as a comprehensive guide for researchers and practitioners to advance online learning approaches for influence maximization in complex, dynamic networks.
Abstract
In this survey, we offer an extensive overview of the Online Influence Maximization (IM) problem by covering both theoretical aspects and practical applications. For the integrity of the article and because the online algorithm takes an offline oracle as a subroutine, we first make a clear definition of the Offline IM problem and summarize those commonly used Offline IM algorithms, which include traditional approximation or heuristic algorithms and ML-based algorithms. Then, we give a standard definition of the Online IM problem and a basic Combinatorial Multi-Armed Bandit (CMAB) framework, CMAB-T. Here, we summarize three types of feedback in the CMAB model and discuss in detail how to study the Online IM problem based on the CMAB-T model. This paves the way for solving the Online IM problem by using online learning methods. Furthermore, we have covered almost all Online IM algorithms up to now, focusing on characteristics and theoretical guarantees of online algorithms for different feedback types. Here, we elaborately explain their working principle and how to obtain regret bounds. Besides, we also collect plenty of innovative ideas about problem definition and algorithm designs and pioneering works for variants of the Online IM problem and their corresponding algorithms. Finally, we encapsulate current challenges and outline prospective research directions from four distinct perspectives.