Spectral bandits for smooth graph functions with applications in recommender systems

2026-05-19

AI Summary

This work addresses the problem of online recommendation on graph-structured items under the assumption that the reward function is smooth over the graph. The authors propose a scalable spectral bandit algorithm that effectively controls cumulative regret as the number of nodes grows. By modeling items as graph nodes and leveraging the smoothness of rewards, they introduce the notion of the graph’s effective dimension and design two algorithms whose complexity scales linearly with this dimension, substantially reducing computational overhead in large-scale settings. Built upon spectral graph theory and smooth function modeling, the proposed method accurately estimates user preferences over thousands of items using only dozens of node-level feedback signals, demonstrating both high efficiency and strong scalability in real-world recommendation scenarios.

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 recommended item 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 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 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 nodes evaluations.

Problem

• spectral bandits
• smooth graph functions
• recommender systems
• online learning
• cumulative regret

Innovation

• spectral bandits
• smooth graph functions
• effective dimension
• online learning
• recommender systems