Online Competitive Influence Maximization

TL;DR

This paper introduces a new online competitive influence maximization problem in social networks, addressing the challenge of competing influences with unknown parameters and proposing algorithms with proven regret bounds.

Contribution

It formulates the OCIM problem within a CMAB framework, proves the TPM condition holds despite competition, and develops algorithms with sublinear regret guarantees.

Findings

Algorithms achieve sublinear Bayesian and frequentist regret.

The TPM condition is validated for the competitive setting.

Experimental results confirm algorithm effectiveness.

Abstract

Online influence maximization has attracted much attention as a way to maximize influence spread through a social network while learning the values of unknown network parameters. Most previous works focus on single-item diffusion. In this paper, we introduce a new Online Competitive Influence Maximization (OCIM) problem, where two competing items (e.g., products, news stories) propagate in the same network and influence probabilities on edges are unknown. We adopt a combinatorial multi-armed bandit (CMAB) framework for OCIM, but unlike the non-competitive setting, the important monotonicity property (influence spread increases when influence probabilities on edges increase) no longer holds due to the competitive nature of propagation, which brings a significant new challenge to the problem. We provide a nontrivial proof showing that the Triggering Probability Modulated (TPM) condition for CMAB still holds in OCIM, which is instrumental for our proposed algorithms OCIM-TS and OCIM-OFU to achieve sublinear Bayesian and frequentist regret, respectively. We also design an OCIM-ETC algorithm that requires less feedback and easier offline computation, at the expense of a worse frequentist regret bound. Experimental evaluations demonstrate the effectiveness of our algorithms.