Influence Maximization (IM) in temporal graphs focuses on identifying influential "seeds" that are pivotal for maximizing network expansion. We advocate defining these seeds through Influence Propagation Paths (IPPs), which is essential for scaling up the network. Our focus lies in efficiently labeling IPPs and accurately predicting these seeds, while addressing the often-overlooked cold-start issue prevalent in temporal networks. Our strategy introduces a motif-based labeling method and a tensorized Temporal Graph Network (TGN) tailored for multi-relational temporal graphs, bolstering prediction accuracy and computational efficiency. Moreover, we augment cold-start nodes with new neighbors from historical data sharing similar IPPs. The recommendation system within an online team-based gaming environment presents subtle impact on the social network, forming multi-relational (i.e., weak and strong) temporal graphs for our empirical IM study. We conduct offline experiments to assess prediction accuracy and model training efficiency, complemented by online A/B testing to validate practical network growth and the effectiveness in addressing the cold-start issue.

The Influence Maximization (IM) problem aims to find a small set of influential users to maximize their influence spread in a social network. Traditional methods rely on fixed diffusion models with known parameters, limiting their generalization to real-world scenarios. In contrast, graph representation learning-based methods have gained wide attention for overcoming this limitation by learning user representations to capture influence characteristics. However, existing studies are built on Euclidean space, which fails to effectively capture the latent hierarchical features of social influence distribution. As a result, users' influence spread cannot be effectively measured through the learned representations. To alleviate these limitations, we propose HIM, a novel diffusion model agnostic method that leverages hyperbolic representation learning to estimate users' potential influence spread from social propagation data. HIM consists of two key components. First, a hyperbolic influence representation module encodes influence spread patterns from network structure and historical influence activations into expressive hyperbolic user representations. Hence, the influence magnitude of users can be reflected through the geometric properties of hyperbolic space, where highly influential users tend to cluster near the space origin. Second, a novel adaptive seed selection module is developed to flexibly and effectively select seed users using the positional information of learned user representations. Extensive experiments on five network datasets demonstrate the superior effectiveness and efficiency of our method for the IM problem with unknown diffusion model parameters, highlighting its potential for large-scale real-world social networks.

The influence maximization (IM) problem involves identifying a set of key individuals in a social network who can maximize the spread of influence through their network connections. With the advent of geometric deep learning on graphs, great progress has been made towards better solutions for the IM problem. In this paper, we focus on the dynamic non-progressive IM problem, which considers the dynamic nature of real-world social networks and the special case where the influence diffusion is non-progressive, i.e., nodes can be activated multiple times. We first extend an existing diffusion model to capture the non-progressive influence propagation in dynamic social networks. We then propose the method, DNIMRL, which employs deep reinforcement learning and dynamic graph embedding to solve the dynamic non-progressive IM problem. In particular, we propose a novel algorithm that effectively leverages graph embedding to capture the temporal changes of dynamic networks and seamlessly integrates with deep reinforcement learning. The experiments, on different types of real-world social network datasets, demonstrate that our method outperforms state-of-the-art baselines.

The Influence Maximization (IM) problem seeks to discover the set of nodes in a graph that can spread the information propagation at most. This problem is known to be NP-hard, and it is usually studied by maximizing the influence (spread) and, optionally, optimizing a second objective, such as minimizing the seed set size or maximizing the influence fairness. However, in many practical scenarios multiple aspects of the IM problem must be optimized at the same time. In this work, we propose a first case study where several IM-specific objective functions, namely budget, fairness, communities, and time, are optimized on top of the maximization of influence and minimization of the seed set size. To this aim, we introduce MOEIM (Many-Objective Evolutionary Algorithm for Influence Maximization) a Multi-Objective Evolutionary Algorithm (MOEA) based on NSGA-II incorporating graph-aware operators and a smart initialization. We compare MOEIM in two experimental settings, including a total of nine graph datasets, two heuristic methods, a related MOEA, and a state-of-the-art Deep Learning approach. The experiments show that MOEIM overall outperforms the competitors in most of the tested many-objective settings. To conclude, we also investigate the correlation between the objectives, leading to novel insights into the topic. The codebase is available at https://github.com/eliacunegatti/MOEIM.

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.

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 an 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.

Most solutions to the inventory management problem assume a centralization of information that is incompatible with organisational constraints in real supply chain networks. The inventory management problem is a well-known planning problem in operations research, concerned with finding the optimal re-order policy for nodes in a supply chain. While many centralized solutions to the problem exist, they are not applicable to real-world supply chains made up of independent entities. The problem can however be naturally decomposed into sub-problems, each associated with an independent entity, turning it into a multi-agent system. Therefore, a decentralized data-driven solution to inventory management problems using multi-agent reinforcement learning is proposed where each entity is controlled by an agent. Three multi-agent variations of the proximal policy optimization algorithm are investigated through simulations of different supply chain networks and levels of uncertainty. The centralized training decentralized execution framework is deployed, which relies on offline centralization during simulation-based policy identification, but enables decentralization when the policies are deployed online to the real system. Results show that using multi-agent proximal policy optimization with a centralized critic leads to performance very close to that of a centralized data-driven solution and outperforms a distributed model-based solution in most cases while respecting the information constraints of the system.

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-the-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. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve 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 IM problem with DRL trained their models on subgraphs of the whole network, and then tested 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 with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.

Influence Maximization (IM) is the task of selecting a fixed number of seed nodes in a given network to maximize dissemination benefits. Although the research for efficient algorithms has been dedicated recently, it is usually neglected to further explore the graph structure and the objective function inherently. With this motivation, we take the first attempt on the hypergraph-based IM with a novel causal objective. We consider the case that each hypergraph node carries specific attributes with Individual Treatment Effect (ITE), namely the change of potential outcomes before/after infections in a causal inference perspective. In many scenarios, the sum of ITEs of the infected is a more reasonable objective for influence spread, whereas it is difficult to achieve via current IM algorithms. In this paper, we introduce a new algorithm called \textbf{CauIM}. We first recover the ITE of each node with observational data and then conduct a weighted greedy algorithm to maximize the sum of ITEs of the infected. Theoretically, we mainly present the generalized lower bound of influence spread beyond the well-known $(1-\frac{1}{e})$ optimal guarantee and provide the robustness analysis. Empirically, in real-world experiments, we demonstrate the effectiveness and robustness of \textbf{CauIM}. It outperforms the previous IM and randomized methods significantly.

In this paper, we consider the inventory management (IM) problem where we need to make replenishment decisions for a large number of stock keeping units (SKUs) to balance their supply and demand. In our setting, the constraint on the shared resources (such as the inventory capacity) couples the otherwise independent control for each SKU. We formulate the problem with this structure as Shared-Resource Stochastic Game (SRSG)and propose an efficient algorithm called Context-aware Decentralized PPO (CD-PPO). Through extensive experiments, we demonstrate that CD-PPO can accelerate the learning procedure compared with standard MARL algorithms.