Spectral bandits for smooth graph functions

2026-04-20

AI Summary

This work addresses the problem of online multi-armed bandits with smooth rewards over graph structures, where the expected rewards of nodes—such as recommendation items—exhibit smoothness with respect to the underlying graph. The authors introduce the key notion of “graph effective dimension” and leverage spectral graph theory together with the smoothness assumption to design two efficient algorithms. These algorithms achieve computational complexity that scales linearly or sublinearly with the effective dimension, thereby eliminating dependence on the total number of nodes. Empirical results on real-world content recommendation tasks demonstrate that user preferences over thousands of items can be accurately estimated using feedback from only dozens of nodes, substantially enhancing scalability and learning efficiency in large-scale graph settings.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of nodes evaluations.

Problem

• spectral bandits
• smooth graph functions
• online learning
• content-based recommendation
• cumulative regret

Innovation

• spectral bandits
• smooth graph functions
• effective dimension
• online learning on graphs
• cumulative regret