Spectral bandits

2026-04-28

AI Summary

This work addresses the problem of online recommendation on graph-structured data with smooth reward functions, aiming to achieve low cumulative regret in the graph bandit setting without dependence on the total number of nodes. Leveraging spectral graph theory and graph signal processing, the authors introduce an “effective dimension” to characterize the smoothness of rewards over the graph and develop novel algorithms whose computational complexity scales linearly or sublinearly with this effective dimension. By integrating ideas from semi-supervised learning, the proposed approach constructs highly accurate user preference estimators for thousands of items using only dozens of user interactions, substantially improving both scalability and sample efficiency in content recommendation tasks.

Abstract

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this work, 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 of an undirected graph and its expected rating is similar to the one of 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 three algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of node evaluations.

Problem

• spectral bandits
• graph smoothness
• online recommendation
• cumulative regret
• effective dimension

Innovation

• spectral bandits
• graph smoothness
• effective dimension
• online learning
• content-based recommendation