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.

研究如何在具有图结构数据的情况下，使用置换不变量将图神经网络用于奖励函数的估计，并通过设计一个分阶段消去算法实现亚线性的后悔保证。

图神经网络赌博机

Graph Neural Network Bandits

Representations of sets are challenging to learn because operations on sets
should be permutation-invariant. To this end, we propose a
Permutation-Optimisation module that learns how to permute a set end-to-end.
The permuted set can be further processed to learn a permutation-invariant
representation of that set, avoiding a bottleneck in traditional set models. We
demonstrate our model's ability to learn permutations and set representations
with either explicit or implicit supervision on four datasets, on which we
achieve state-of-the-art results: number sorting, image mosaics, classification
from image mosaics, and visual question answering.

探讨了学习集合表示的挑战性。通过引入置换优化模块来解决这一问题，该模块学习如何对一个集合进行置换，通过对置换后的集合进行处理，以避免传统集合模型中的瓶颈，进而实现学习该集合具有不变性的表征。通过对数排序，图像马赛克，图像马赛克分类和视觉问答等四个数据集进行明确或隐式监督的训练，证明了我们模型的置换和集合表示学习能力。取得了最先进的结果。