PageRank Bandits for Link Prediction

TL;DR

A novel fusion algorithm, PRB (PageRank Bandits), which is the first to combine contextual bandits with PageRank for collaborative exploitation and exploration and also introduces a new reward formulation and provides a theoretical performance guarantee for PRB.

Abstract

Link prediction is a critical problem in graph learning with broad applications such as recommender systems and knowledge graph completion. Numerous research efforts have been directed at solving this problem, including approaches based on similarity metrics and Graph Neural Networks (GNN). However, most existing solutions are still rooted in conventional supervised learning, which makes it challenging to adapt over time to changing customer interests and to address the inherent dilemma of exploitation versus exploration in link prediction. To tackle these challenges, this paper reformulates link prediction as a sequential decision-making process, where each link prediction interaction occurs sequentially. We propose a novel fusion algorithm, PRB (PageRank Bandits), which is the first to combine contextual bandits with PageRank for collaborative exploitation and exploration. We also introduce a new reward formulation and provide a theoretical performance guarantee for PRB. Finally, we extensively evaluate PRB in both online and offline settings, comparing it with bandit-based and graph-based methods. The empirical success of PRB demonstrates the value of the proposed fusion approach. Our code is released at https://github.com/jiaruzouu/PRB.

Figures (7)

• Figure 1: Transforming Node Classification to Link Prediction. Consider a binary node classification problem. In the left figure, given a graph, the learner tries to classify node 4 into one of two classes. First, we add two supernodes to the graph, each representing one of the classes. The node classification problem is then transformed into predicting links between node 4 and the two supernodes in the right figure. Suppose the learner predicts that a link will exist between node 4 and supernode 0. If node 4 belongs to Class 0, the reward is 1, and an edge is added between node 4 and supernode 0; otherwise, the reward is 0, and an edge is added between node 4 and supernode 1.
• Figure 2: Regret comparison of bandit-based methods on online link prediction datasets (average of 10 runs with standard deviation in shadow, detailed in Table \ref{['tab:bandit-based res']}).
• Figure 3: Regret comparison of bandit-based methods on online node classification datasets (average of 10 runs with standard deviation in shadow, detailed in Table \ref{['tab:node classification res']}.
• Figure 4: Running time comparison of PRB and bandit-based baselines.
• Figure 5: Proportion of running time for PRB-Greedy (left) and PRB (right) between exploitation-exploration and random walk.

Theorems & Definitions (27)

• Definition 5.1: NTK ntk2018neuralwang2021neural
• Theorem 5.1
• Lemma E.1
• Lemma E.2
• Lemma E.3
• Lemma E.4: Almost Convexity
• Lemma E.5: User Trajectory Ball
• Lemma E.6: Instance-dependent Loss Bound
• Lemma E.7
• proof