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This paper tackles a multi-agent bandit setting where $M$ agents cooperate together to solve the same instance of a $K$-armed stochastic bandit problem. The agents are \textit{heterogeneous}: each agent has limited access to a local subset of arms and the agents are asynchronous with different gaps between decision-making rounds. The goal for each agent is to find its optimal local arm, and agents can cooperate by sharing their observations with others. While cooperation between agents improves the performance of learning, it comes with an additional complexity of communication between agents. For this heterogeneous multi-agent setting, we propose two learning algorithms, \ucbo and \AAE. We prove that both algorithms achieve order-optimal regret, which is $O\left(\sum_{i:\tilde{\Delta}_i>0} \log T/\tilde{\Delta}_i\right)$, where $\tilde{\Delta}_i$ is the minimum suboptimality gap between the reward mean of arm $i$ and any local optimal arm. In addition, a careful selection of the valuable information for cooperation, \AAE achieves a low communication complexity of $O(\log T)$. Last, numerical experiments verify the efficiency of both algorithms.

Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms, is \emph{probability sampling}. It creates a sampled data set by including each data point from the original data set with a known probability. Although the benefit of running machine learning algorithms on the reduced data set is obvious, one major concern is that the performance of the solution obtained from samples might be much worse than that of the optimal solution when using the full data set. In this paper, we examine the performance loss caused by probability sampling in the context of adaptive submodular maximization. We consider a simple probability sampling method which selects each data point with probability at least $r\in[0,1]$. If we set $r=1$, our problem reduces to finding a solution based on the original full data set. We define sampling gap as the largest ratio between the optimal solution obtained from the full data set and the optimal solution obtained from the samples, over independence systems. Our main contribution is to show that if the sampling probability of each data point is at least $r$ and the utility function is policywise submodular, then the sampling gap is both upper bounded and lower bounded by $1/r$. We show that the property of policywise submodular can be found in a wide range of real-world applications, including pool-based active learning and adaptive viral marketing.

In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the Euler-Maruyama discretization of the Langevin equation, where the forward-backward envelope is used to deal with the non-smooth part of the dynamics. An advantage of this envelope, when compared to widely-used Moreu-Yoshida one and the MYULA algorithm, is that it maintains the MAP estimator of the original non-smooth distribution. We also study a number of numerical experiments that corroborate that support our theoretical findings.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. In this work, we propose a relational message passing method for knowledge graph completion. Different from existing embedding-based methods, relational message passing only considers edge features (i.e., relation types) without entity IDs in the knowledge graph, and passes relational messages among edges iteratively to aggregate neighborhood information. Specifically, two kinds of neighborhood topology are modeled for a given entity pair under the relational message passing framework: (1) Relational context, which captures the relation types of edges adjacent to the given entity pair; (2) Relational paths, which characterize the relative position between the given two entities in the knowledge graph. The two message passing modules are combined together for relation prediction. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that, our method PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. PathCon is also shown applicable to inductive settings where entities are not seen in training stage, and it is able to provide interpretable explanations for the predicted results. The code and all datasets are available at //github.com/hwwang55/PathCon.

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs) - topological objects generalising graphs to higher dimensions. To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline. Additionally, we implement a library for message passing on simplicial complexes that we envision to release in due course.

Graph Convolution Networks (GCNs) manifest great potential in recommendation. This is attributed to their capability on learning good user and item embeddings by exploiting the collaborative signals from the high-order neighbors. Like other GCN models, the GCN based recommendation models also suffer from the notorious over-smoothing problem - when stacking more layers, node embeddings become more similar and eventually indistinguishable, resulted in performance degradation. The recently proposed LightGCN and LR-GCN alleviate this problem to some extent, however, we argue that they overlook an important factor for the over-smoothing problem in recommendation, that is, high-order neighboring users with no common interests of a user can be also involved in the user's embedding learning in the graph convolution operation. As a result, the multi-layer graph convolution will make users with dissimilar interests have similar embeddings. In this paper, we propose a novel Interest-aware Message-Passing GCN (IMP-GCN) recommendation model, which performs high-order graph convolution inside subgraphs. The subgraph consists of users with similar interests and their interacted items. To form the subgraphs, we design an unsupervised subgraph generation module, which can effectively identify users with common interests by exploiting both user feature and graph structure. To this end, our model can avoid propagating negative information from high-order neighbors into embedding learning. Experimental results on three large-scale benchmark datasets show that our model can gain performance improvement by stacking more layers and outperform the state-of-the-art GCN-based recommendation models significantly.

We present a hierarchical neural message passing architecture for learning on molecular graphs. Our model takes in two complementary graph representations: the raw molecular graph representation and its associated junction tree, where nodes represent meaningful clusters in the original graph, e.g., rings or bridged compounds. We then proceed to learn a molecule's representation by passing messages inside each graph, and exchange messages between the two representations using a coarse-to-fine and fine-to-coarse information flow. Our method is able to overcome some of the restrictions known from classical GNNs, like detecting cycles, while still being very efficient to train. We validate its performance on the ZINC dataset and datasets stemming from the MoleculeNet benchmark collection.

Question answering over knowledge graphs (KGQA) has evolved from simple single-fact questions to complex questions that require graph traversal and aggregation. We propose a novel approach for complex KGQA that uses unsupervised message passing, which propagates confidence scores obtained by parsing an input question and matching terms in the knowledge graph to a set of possible answers. First, we identify entity, relationship, and class names mentioned in a natural language question, and map these to their counterparts in the graph. Then, the confidence scores of these mappings propagate through the graph structure to locate the answer entities. Finally, these are aggregated depending on the identified question type. This approach can be efficiently implemented as a series of sparse matrix multiplications mimicking joins over small local subgraphs. Our evaluation results show that the proposed approach outperforms the state-of-the-art on the LC-QuAD benchmark. Moreover, we show that the performance of the approach depends only on the quality of the question interpretation results, i.e., given a correct relevance score distribution, our approach always produces a correct answer ranking. Our error analysis reveals correct answers missing from the benchmark dataset and inconsistencies in the DBpedia knowledge graph. Finally, we provide a comprehensive evaluation of the proposed approach accompanied with an ablation study and an error analysis, which showcase the pitfalls for each of the question answering components in more detail.

Precise user and item embedding learning is the key to building a successful recommender system. Traditionally, Collaborative Filtering(CF) provides a way to learn user and item embeddings from the user-item interaction history. However, the performance is limited due to the sparseness of user behavior data. With the emergence of online social networks, social recommender systems have been proposed to utilize each user's local neighbors' preferences to alleviate the data sparsity for better user embedding modeling. We argue that, for each user of a social platform, her potential embedding is influenced by her trusted users. As social influence recursively propagates and diffuses in the social network, each user's interests change in the recursive process. Nevertheless, the current social recommendation models simply developed static models by leveraging the local neighbors of each user without simulating the recursive diffusion in the global social network, leading to suboptimal recommendation performance. In this paper, we propose a deep influence propagation model to stimulate how users are influenced by the recursive social diffusion process for social recommendation. For each user, the diffusion process starts with an initial embedding that fuses the related features and a free user latent vector that captures the latent behavior preference. The key idea of our proposed model is that we design a layer-wise influence propagation structure to model how users' latent embeddings evolve as the social diffusion process continues. We further show that our proposed model is general and could be applied when the user~(item) attributes or the social network structure is not available. Finally, extensive experimental results on two real-world datasets clearly show the effectiveness of our proposed model, with more than 13% performance improvements over the best baselines.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.