Online Influence Maximization under Independent Cascade Model with Semi-Bandit Feedback

TL;DR

This paper introduces IMLinUCB, a novel algorithm for online influence maximization in social networks under the independent cascade model, effectively handling combinatorial actions and limited feedback to learn influential nodes.

Contribution

It presents the first regret bounds for online influence maximization with semi-bandit feedback, incorporating network topology and edge probabilities, and demonstrates the algorithm's efficiency and effectiveness.

Findings

Regret bounds are polynomial in network parameters.

IMLinUCB scales well with network size and complexity.

Linear generalization improves performance in real-world scenarios.

Abstract

We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based algorithm. Our bounds on the cumulative regret are polynomial in all quantities of interest, achieve near-optimal dependence on the number of interactions and reflect the topology of the network and the activation probabilities of its edges, thereby giving insights on the problem complexity. To the best of our knowledge, these are the first such results. Our experiments show that in several representative graph topologies, the regret of IMLinUCB scales as suggested by our upper bounds. IMLinUCB permits linear generalization and thus is both statistically and computationally suitable for large-scale problems. Our experiments also show that IMLinUCB with linear generalization can lead to low regret in real-world online influence maximization.