Spectral bandits for smooth graph functions with applications in recommender systems

2026-05-21 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, medium

Summary

Spectral Bandits is a novel framework for online learning on graphs where expected payoffs for "arms" (nodes) are smooth functions, meaning neighboring nodes have similar values. This approach addresses challenges in applications like content-based recommendation systems and targeted advertising in social networks, where the number of nodes (N) can be very large. The framework leverages the property that smooth graph functions can be represented as linear combinations of graph Laplacian eigenvectors. The authors introduce the concept of an "effective dimension" (d), which is significantly smaller than N in real-world graphs. They propose two algorithms designed to scale linearly with this effective dimension, rather than the full graph dimension. Experiments on a real-world content recommendation task demonstrated that these algorithms can learn accurate user preference estimators for thousands of items using only tens of node evaluations.

Key takeaway

For Machine Learning Engineers building recommender systems or targeted advertising platforms on large graphs, consider adopting the Spectral Bandits framework. This approach allows you to learn accurate user preferences for thousands of items from minimal feedback, scaling efficiently with the graph's effective dimension rather than its full size. You can significantly reduce data collection needs and computational overhead compared to traditional bandit methods.

Key insights

Spectral bandits efficiently learn smooth graph functions by utilizing an "effective dimension" for scalable online recommendation.

Principles

• Smooth graph functions are linear combinations of graph Laplacian eigenvectors.
• Effective dimension d is small in real-world graphs.
• Algorithms can scale linearly with effective dimension, not node count.

Method

The proposed algorithms select a node at time t, observe a noisy payoff, and update a model of the smooth preference function on the graph, aiming to minimize cumulative regret.

In practice

• Apply to content-based recommender systems.
• Use for targeted advertising in social networks.

Topics

• Spectral Bandits
• Recommender Systems
• Graph Functions
• Online Learning
• Effective Dimension
• Graph Laplacian

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.