Online Influence Maximization: Concept and Algorithm

In this survey, we offer an extensive overview of the Online Influence Maximization (IM) problem by covering both theoretical aspects and practical applications. For the integrity of the article and because the online algorithm takes an offline oracle as a subroutine, we first make a clear definition of the Offline IM problem and summarize those commonly used Offline IM algorithms, which include traditional approximation or heuristic algorithms and ML-based algorithms. Then, we give a standard definition of the Online IM problem and a basic Combinatorial Multi-Armed Bandit (CMAB) framework, CMAB-T. Here, we summarize three types of feedback in the CMAB model and discuss in detail how to study the Online IM problem based on the CMAB-T model. This paves the way for solving the Online IM problem by using online learning methods. Furthermore, we have covered almost all Online IM algorithms up to now, focusing on characteristics and theoretical guarantees of online algorithms for different feedback types. Here, we elaborately explain their working principle and how to obtain regret bounds. Besides, we also collect plenty of innovative ideas about problem definition and algorithm designs and pioneering works for variants of the Online IM problem and their corresponding algorithms. Finally, we encapsulate current challenges and outline prospective research directions from four distinct perspectives.

DSCom: A Data-Driven Self-Adaptive Community-Based Framework for Influence Maximization in Social Networks

Influence maximization aims to find a subset of seeds that maximize the influence spread under a given budget. In this paper, we mainly address the data-driven version of this problem, where the diffusion model is not given but needs to be inferred from the history cascades. Several previous works have addressed this topic in a statistical way and provided efficient algorithms with theoretical guarantee. However, in their settings, though the diffusion parameters are inferred, they still need users to preset the diffusion model, which can be an intractable problem in real-world practices. In this paper, we reformulate the problem on the attributed network and leverage the node attributes to estimate the closeness between the connected nodes. Specifically, we propose a machine learning-based framework, named DSCom, to address this problem in a heuristic way. Under this framework, we first infer the users' relationship from the diffusion dataset through attention mechanism and then leverage spectral clustering to overcome the influence overlap problem in the lack of exact diffusion formula. Compared to the previous theoretical works, we carefully designed empirical experiments with parameterized diffusion models based on real-world social networks, which prove the efficiency and effectiveness of our algorithm.

A Modified EXP3 and Its Adaptive Variant in Adversarial Bandits with Multi-User Delayed Feedback

For the adversarial multi-armed bandit problem with delayed feedback, we consider that the delayed feedback results are from multiple users and are unrestricted on internal distribution. As the player picks an arm, feedback from multiple users may not be received instantly yet after an arbitrary delay of time which is unknown to the player in advance. For different users in a round, the delays in feedback have no latent correlation. Thus, we formulate an adversarial multi-armed bandit problem with multi-user delayed feedback and design a modified EXP3 algorithm named MUD-EXP3, which makes a decision at each round by considering the importance-weighted estimator of the received feedback from different users. On the premise of known terminal round index $T$, the number of users $M$, the number of arms $N$, and upper bound of delay $d_{max}$, we prove a regret of $\mathcal{O}(\sqrt{TM^2\ln{N}(N\mathrm{e}+4d_{max})})$. Furthermore, for the more common case of unknown $T$, an adaptive algorithm named AMUD-EXP3 is proposed with a sublinear regret with respect to $T$. Finally, extensive experiments are conducted to indicate the correctness and effectiveness of our algorithms.

A Fast Task Offloading Optimization Framework for IRS-Assisted Multi-Access Edge Computing System

Terahertz communication networks and intelligent reflecting surfaces exhibit significant potential in advancing wireless networks, particularly within the domain of aerial-based multi-access edge computing systems. These technologies enable efficient offloading of computational tasks from user electronic devices to Unmanned Aerial Vehicles or local execution. For the generation of high-quality task-offloading allocations, conventional numerical optimization methods often struggle to solve challenging combinatorial optimization problems within the limited channel coherence time, thereby failing to respond quickly to dynamic changes in system conditions. To address this challenge, we propose a deep learning-based optimization framework called Iterative Order-Preserving policy Optimization (IOPO), which enables the generation of energy-efficient task-offloading decisions within milliseconds. Unlike exhaustive search methods, IOPO provides continuous updates to the offloading decisions without resorting to exhaustive search, resulting in accelerated convergence and reduced computational complexity, particularly when dealing with complex problems characterized by extensive solution spaces. Experimental results demonstrate that the proposed framework can generate energy-efficient task-offloading decisions within a very short time period, outperforming other benchmark methods.

FedCL: Federated Multi-Phase Curriculum Learning to Synchronously Correlate User Heterogeneity

Federated Learning (FL) is a new decentralized learning used for training machine learning algorithms where a global model iteratively gathers the parameters of local models but does not access their local data. A key challenge in FL is to handle the heterogeneity of local data distribution, resulting in a drifted global model, which is hard to converge. To cope with this challenge, current methods adopt different strategies like knowledge distillation, weighted model aggregation, and multi-task learning, as regulation. We refer to these approaches as asynchronous FL since they align user models in either a local or post-hoc manner where model drift has already happened or has been underestimated. In this paper, we propose an active and synchronous correlation approach to solve the challenge of user heterogeneity in FL. Specifically, we aim to approximate FL as the standard deep learning by actively and synchronously scheduling user learning pace in each round with a dynamic multi-phase curriculum. A global curriculum ensembles all user curriculum on its server by the auto-regressive auto-encoder. Then the global curriculum is divided into multiple phases and broadcast to users to measure and align the domain-agnostic learning pace. Empirical studies demonstrate that our approach equips FL with state-of-the-art generalization performance over existing asynchronous approaches, even facing severe user heterogeneity.

A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization

Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and \#P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, the technology based on Machine Learning (ML) has achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out.

ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning

Online social platforms have become more and more popular, and the dissemination of information on social networks has attracted wide attention of the industries and academia. Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. With the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, a lot of works has focused on exploiting DRL to solve the combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve the IM problem with DRL trained their models on the subgraph of the whole network, and then tested their performance on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs and tested on completely different networks, and can obtain results that are very close to the state-of-the-art methods. In addition, our model is trained with a small budget, and it can perform well under various large budgets in the test, showing strong generalization ability. Finally, we conduct entensive experiments on synthetic and realistic datasets, and the experimental results prove the effectiveness and superiority of our model.

Graph Representation Learning for Popularity Prediction Problem: A Survey

The online social platforms, like Twitter, Facebook, LinkedIn and WeChat, have grown really fast in last decade and have been one of the most effective platforms for people to communicate and share information with each other. Due to the "word of mouth" effects, information usually can spread rapidly on these social media platforms. Therefore, it is important to study the mechanisms driving the information diffusion and quantify the consequence of information spread. A lot of efforts have been focused on this problem to help us better understand and achieve higher performance in viral marketing and advertising. On the other hand, the development of neural networks has blossomed in the last few years, leading to a large number of graph representation learning (GRL) models. Compared to traditional models, GRL methods are often shown to be more effective. In this paper, we present a comprehensive review for existing works using GRL methods for popularity prediction problem, and categorize related literatures into two big classes, according to their mainly used model and techniques: embedding-based methods and deep learning methods. Deep learning method is further classified into six small classes: convolutional neural networks, graph convolutional networks, graph attention networks, graph neural networks, recurrent neural networks, and reinforcement learning. We compare the performance of these different models and discuss their strengths and limitations. Finally, we outline the challenges and future chances for popularity prediction problem.

Continuous Profit Maximization: A Study of Unconstrained Dr-submodular Maximization

Profit maximization (PM) is to select a subset of users as seeds for viral marketing in online social networks, which balances between the cost and the profit from influence spread. We extend PM to that under the general marketing strategy, and form continuous profit maximization (CPM-MS) problem, whose domain is on integer lattices. The objective function of our CPM-MS is dr-submodular, but non-monotone. It is a typical case of unconstrained dr-submodular maximization (UDSM) problem, and take it as a starting point, we study UDSM systematically in this paper, which is very different from those existing researcher. First, we introduce the lattice-based double greedy algorithm, which can obtain a constant approximation guarantee. However, there is a strict and unrealistic condition that requiring the objective value is non-negative on the whole domain, or else no theoretical bounds. Thus, we propose a technique, called lattice-based iterative pruning. It can shrink the search space effectively, thereby greatly increasing the possibility of satisfying the non-negative objective function on this smaller domain without losing approximation ratio. Then, to overcome the difficulty to estimate the objective value of CPM-MS, we adopt reverse sampling strategies, and combine it with lattice-based double greedy, including pruning, without losing its performance but reducing its running time. The entire process can be considered as a general framework to solve the UDSM problem, especially for applying to social networks. Finally, we conduct experiments on several real datasets to evaluate the effectiveness and efficiency of our proposed algorithms.