Spectral bandits for smooth graph functions with applications in recommender systems

TL;DR

This paper introduces spectral bandit algorithms for smooth graph functions, enabling efficient online recommendations by leveraging the graph's effective dimension to reduce regret.

Contribution

It proposes two scalable algorithms that utilize the effective dimension of graphs, improving online learning efficiency in content recommendation tasks.

Findings

Algorithms scale linearly with the effective dimension.

Good preference estimations achieved from limited node evaluations.

Experimental results demonstrate practical effectiveness in real-world recommendation systems.

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.