Revealing graph bandits for maximizing local influence

2026-05-01

AI Summary

This work addresses the problem of identifying the most locally influential nodes in a graph with minimal query complexity when no prior knowledge of the graph structure is available. To this end, it introduces a novel graph bandit setting in which the graph is revealed incrementally through sequential active exploration: at each round, an algorithm selects a node and observes its stochastic influence spread. The core contribution is BARE, a strategy that integrates multi-armed bandit principles, an adaptive graph discovery mechanism, and stochastic influence feedback—requiring no structural priors. Theoretical analysis shows that BARE achieves a regret bound governed by a “discoverable dimension,” which is typically much smaller than the total number of nodes, thereby substantially improving sample efficiency over conventional methods that rely on known graph structures.

Abstract

We study a graph bandit setting where the objective of the learner is to detect the most influential node of a graph by requesting as little information from the graph as possible. One of the relevant applications for this setting is marketing in social networks, where the marketer aims at finding and taking advantage of the most influential customers. The existing approaches for bandit problems on graphs require either partial or complete knowledge of the graph. In this paper, we do not assume any knowledge of the graph, but we consider a setting where it can be gradually discovered in a sequential and active way. At each round, the learner chooses a node of the graph and the only information it receives is a stochastic set of the nodes that the chosen node is currently influencing. To address this setting, we propose BARE, a bandit strategy for which we prove a regret guarantee that scales with the detectable dimension, a problem dependent quantity that is often much smaller than the number of nodes.

Problem

• graph bandits
• influence maximization
• sequential discovery
• active learning
• social networks

Innovation

• graph bandits
• influence maximization
• active graph discovery
• detectable dimension
• BARE algorithm