Bandit Samplers for Training Graph Neural Networks

TL;DR

This paper introduces a novel bandit-based sampling algorithm for training graph neural networks that adaptively balances exploration and exploitation to minimize variance, outperforming existing methods especially for models with learned weights.

Contribution

It formulates the sampling variance optimization as an adversarial bandit problem and provides a theoretically grounded algorithm that approaches optimal variance within a factor of 3.

Findings

The proposed method asymptotically approaches the optimal variance.

The algorithm demonstrates improved efficiency and effectiveness on multiple datasets.

It extends variance reduction techniques to more general GNNs like GAT.

Abstract

Several sampling algorithms with variance reduction have been proposed for accelerating the training of Graph Convolution Networks (GCNs). However, due to the intractable computation of optimal sampling distribution, these sampling algorithms are suboptimal for GCNs and are not applicable to more general graph neural networks (GNNs) where the message aggregator contains learned weights rather than fixed weights, such as Graph Attention Networks (GAT). The fundamental reason is that the embeddings of the neighbors or learned weights involved in the optimal sampling distribution are changing during the training and not known a priori, but only partially observed when sampled, thus making the derivation of an optimal variance reduced samplers non-trivial. In this paper, we formulate the optimization of the sampling variance as an adversary bandit problem, where the rewards are related to the node embeddings and learned weights, and can vary constantly. Thus a good sampler needs to acquire variance information about more neighbors (exploration) while at the same time optimizing the immediate sampling variance (exploit). We theoretically show that our algorithm asymptotically approaches the optimal variance within a factor of 3. We show the efficiency and effectiveness of our approach on multiple datasets.