Neural Information Processing Systems http://nips.cc/

However,learningefficiencyon these models should be carefully considered as the huge computation overhead.

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. Perhaps surprisingly, even though 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.

In practice, graph data carries complex information among entities that inevitably evolves over time, and previous static graph neural tangent kernel methods may be stuck in the sub-optimal solution in terms of both effectiveness and efficiency. As a result, extending the advantage of GNTK to temporal graphs becomes a critical problem. To this end, we propose the temporal graph neural tangent kernel, which not only extends the simplicity and interpretation ability of GNTK to the temporal setting but also leads to rigorous temporal graph classification error bounds. Furthermore, we prove that when the input temporal graph grows over time in the number of nodes, our temporal graph neural tangent kernel will converge in the limit to the _graphon_ NTK value, which implies the transferability and robustness of the proposed kernel method, named **Temp**oral **G**raph **N**eural **T**angent **K**ernel with **G**raphon-**G**uaranteed or **Temp-G$^3$NTK**. In addition to the theoretical analysis, we also perform extensive experiments, not only demonstrating the superiority of Temp-G$^3$NTK in the temporal graph classification task, but also showing that Temp-G^3NTK can achieve very competitive performance in node-level tasks like node classification compared with various SOTA graph kernel and representation learning baselines.

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to \emph{infinitely wide} multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.

We thank all reviewers for their valuable feedback and appreciating our technical contributions. First, we discuss more about the relation between GNTKs and GNNs. GNNs with more layers perform better on bioinformatics data is not new, we observed the same trend for GNTKs. We will elaborate more on these connections in the final version. Second, Reviewer #2 raised a great point about computational complexity.

Besides, their convolutional methods are often straightforward and introduce severe loss of graph structure information.

Neural Information Processing Systems http://nips.cc/