Graph Neural Network Bandits

by   Parnian Kassraie, et al.

We consider the bandit optimization problem with the reward function defined over graph-structured data. This problem has important applications in molecule design and drug discovery, where the reward is naturally invariant to graph permutations. The key challenges in this setting are scaling to large domains, and to graphs with many nodes. We resolve these challenges by embedding the permutation invariance into our model. In particular, we show that graph neural networks (GNNs) can be used to estimate the reward function, assuming it resides in the Reproducing Kernel Hilbert Space of a permutation-invariant additive kernel. By establishing a novel connection between such kernels and the graph neural tangent kernel (GNTK), we introduce the first GNN confidence bound and use it to design a phased-elimination algorithm with sublinear regret. Our regret bound depends on the GNTK's maximum information gain, which we also provide a bound for. While the reward function depends on all N node features, our guarantees are independent of the number of graph nodes N. Empirically, our approach exhibits competitive performance and scales well on graph-structured domains.


page 1

page 2

page 3

page 4


Neural Contextual Bandits without Regret

Contextual bandits are a rich model for sequential decision making given...

Finite-Time Analysis of Kernelised Contextual Bandits

We tackle the problem of online reward maximisation over a large finite ...

Characterizing the Expressive Power of Invariant and Equivariant Graph Neural Networks

Various classes of Graph Neural Networks (GNN) have been proposed and sh...

Dual Instrumental Method for Confounded Kernelized Bandits

The contextual bandit problem is a theoretically justified framework wit...

Invariant Layers for Graphs with Nodes of Different Types

Neural networks that satisfy invariance with respect to input permutatio...

A Biased Graph Neural Network Sampler with Near-Optimal Regret

Graph neural networks (GNN) have recently emerged as a vehicle for apply...

Adversarial Stein Training for Graph Energy Models

Learning distributions over graph-structured data is a challenging task ...

Please sign up or login with your details

Forgot password? Click here to reset