Learning representation of the enclosing subgraph of node pairs is recognized as an efficient approach for link-oriented prediction tasks in network applications. The core challenge within this subgraph encoding approach is how to effectively distinguish and then properly aggregate the contribution of nodes in the subgraph into a single vector to indicate the relation between the target node pair. In this work, we propose a novel sphere-based subgraph encoding architecture, namely BS-SubGNN, to address the challenge. In detail, we design two key building blocks, including Bicentric Sphere Node Labeling (BSNL) and Bicentric Sphere Subgraph Pooling (BSSP) to assist message passing in BS-SubGNN. BSNL endows each node a label according to the sphere it belongs to in the subgraph to distinguish the contribution of nodes, while BSSP adopts an attention mechanism to aggregate the contribution of nodes in each sphere. Theoretically, we prove that BS-SubGNN can unify existing node distance labeling methods, and yield discriminative node features with less time complexity. We evaluate the performance of BS-SubGNN in link prediction tasks over a variety of network types, including undirected networks, attribute networks, directed networks, and signed directed networks. Our experimental results demonstrate that BS-SubGNN consistently achieves significant performance improvements over the above diverse types of networks. In particular, compared to those methods with a requisite of multi-hop neighborhood information, BS-SubGNN can obtain better performance even when only one-hop neighborhood information of the node pair is utilized.

Industrial Internet of Things (IIoT) systems are vulnerable to cyber-attacks due to their interconnected nature. While federated learning (FL) offers a privacy-preserving approach to intrusion detection, it struggles with data heterogeneity, class imbalance, and adversarial attacks in practical IIoT settings. To address these challenges, this paper introduces HGDS, a FL-based framework that integrates a federated diffusion-based sampler for class rebalancing with a dynamic hypernetwork grouping mechanism for model personalization. The proposed framework further incorporates robust defense strategies, including gradient clipping and anomaly-based client isolation, to mitigate adversarial attacks. Comprehensive evaluations are conducted on four real world datasets. The results demonstrate the superiority of HGDS, which achieves a performance gain of up to 15.3% in F1-score over state-of-the-art benchmarks under non-IID data conditions. Furthermore, the method maintains resilience against both model poisoning and label flipping attacks.

In this article, we consider the problem of equilibrium selection in multiplayer finite potential games with large-size action sets. Traditional learning approaches often require players to traverse the entire action set to evaluate the utility of each action, which can be computationally intensive and inefficient. To overcome this limitation, we leverage the idea of neighborhood search into the game-theoretical learning process for the first time by generating neighborhood candidate action sets for exploration and evaluation. As such, we propose a lightweight log-linear dynamics for efficient equilibrium selection in finite potential games. Asymptotic convergence is proved under both asynchronous and independent revision rules with the help of resistance tree theory. Furthermore, through the multisatellite cooperative task allocation (MSCTA) problem, we elaborate on how to encode the players’ actions and how to generate the neighborhood structure. Simulation results demonstrate that the proposed method significantly outperforms the existing game-theoretic learning methods, notably in terms of solution time.

Inverse reinforcement learning (IRL) aims to infer the reward function from expert demonstrations. However, as IRL techniques are increasingly applied in high-stakes domains such as autonomous driving and military decision-making, reward function leakage has emerged as a critical risk, potentially leading to severe security threats and unintended consequences. To address this challenge, we propose Safe Accelerated Policy Gradient (Safe APG), a method designed to enhance learning security of the demonstrating agent by preventing observers from inferring its reward function. The core idea behind Safe APG is to incorporate a delicately constructed and theoretically guaranteed structural noise into Nesterov’s Accelerated Gradient (NAG) for policy updating, with the goal of concealing critical gradient information from the learning agent as well as keeping the geometric convergence property of NAG. The results from numerical experiments and simulations in reinforcement learning environments demonstrate that the proposed method not only significantly mitigates reward function leakage, but also achieves superior convergence rates even under the perturbation of the introduced structural noise.

Users upload their own WiFi localization request signals to match against the received signal strengths (RSSs) in an offline constructed fingerprint database, thereby obtaining their own geographic location estimates. However, the relationships between the measured signals of users are seldom explored for enhancing the localization accuracy. Furthermore, the tedious site surveys required for building an offline fingerprint database hinder the wider application of this technology. To address the above issues, this article proposes a collaboratively enhanced lightweight WiFi localization algorithm named CBWF+, capable of providing an accurate indoor position with low-overhead fingerprints and collaborative localization. Specifically, we first discretize the area of interest to produce virtual points (VPs), and leverage the concept of circular-boundary-based localization to select a few VPs that share similar signal characteristics with the request signals. Then, important users for collaborative localization are chosen by two new proposed indicators. Next, based on the selection results and the RSS relationships among users, the spatiotemporal characteristics of WiFi signals are used to further filter out VPs that contradict the relationship between RSS and physical location. Finally, the credible VPs are used to obtain a high-accuracy estimate, by a proposed weighting method. The results of the real-world experiments validate the effectiveness of our proposed CBWF+ algorithm, compared to other state-of-the-art approaches (e.g., NN, OCLoc, CBWF, etc.). Specifically, in a 40-m$\times 17$-m real scenario with only 20 reference points (RPs) and 11 access point (APs), our algorithm achieves an average localization accuracy of 2.49 m. Our codes are available at:https://github.com/dadadaray/CBWF2.0.

As industrial control systems become increasingly interconnected with information networks, attackers could exploit vulnerabilities across different system layers to create complex exploit chains to compromise field control elements. As such, security decision-making is of essential importance to maintain the operational security of critical industrial infrastructures. In this paper, we consider the problem of designing cost-effective defense strategies to minimize the risk of successful attack paths. To this end, we propose a non-Markovian security game framework on labeled attack graphs to simulate the attack-defense process in industrial control systems. Compared with existing methods, where the cost of exploiting a vulnerability is considered constant, we consider a more dynamic and realistic case where the exploitation cost is discounted with the number of exploitations. Moreover, a state-decomposition based multi-agent reinforcement learning algorithm is developed to obtain the Nash equilibrium of the proposed non-Markovian security game. A case study on a simulated industrial control system is presented to illustrate the feasibility of the proposed approach. The results demonstrate that the discounting exploitation cost could greatly alter the attack and subsequently the defense strategies. In comparison to traditional static intrusion response approaches, our non-Markovian approach offers a more realistic and adaptive framework to anticipate evolving attack paths and allocate defense resources.

Superdiffusion refers to the faster diffusion process in a multiplex network compared to that in an individual network. In this work, we study how interlayer connectivity affects the diffusion performance of a multiplex network. Based on spectral graph theory, we explore the principles of superdiffusion in multiplex networks. We prove that in a duplex network with identical structures, superdiffusion cannot occur under one-to-one interlayer connections. In addition, we prove that the dissimilarity of the Fiedler vector significantly enhances the network superdiffusion performance, which can lead to superdiffusion when selecting nodes with differential eigenvector components in the Fiedler vector for interlayer connections. We also prove that the upper bound of network diffusion with interlayer crossing-connections is limited by the maximum difference of the eigenvector components in the Fiedler vector. Finally, we verify the effectiveness of the theoretical results by numerical analysis.

WiFi Fingerprint-based Localization (WFL) has recently achieved promising results in the bloom of deep learning techniques. Unfortunately, current studies reveal the great risks of deep-learning models when facing adversarial attacks, raising broader concerns about Deep-learning-based WiFi Fingerprint Localization Models (DFLMs). However, real-world adversarial attacks targeting DFLMs are not fully investigated, making it unclear how to counter this potential threat. In this paper, we take the first step to introduce adversarial examples into the physical world against DFLMs. Specifically, we propose a general attack method named Phy-Adv, consisting of a physical attenuation loss and a differentiable simulation module, the generated adversarial noise could be feasibly produced in the real world and make effects on DFLMs, i.e., misleading the DFLMs from the signal source end. Furthermore, aiming at countering this typical adversarial threat, we propose a Relaxant Multiple Batch Normalization (RMBN) approach, which alleviates the weak robustness of DFLMs by the data-end adaptive training-set segmenting and model-end multiple batch normalization designing. To demonstrate the de facto effectiveness of the proposed physical adversarial examples and the adversarial defense strategy, we conducted extensive experiments on 2 datasets, i.e., BHD and TUT, and multiple deep models, e.g., AlexNet, VGG, and ResNet. The experimental results strongly support that our Phy-Adv shows satisfactory adversarial attacking ability in the physical world, meanwhile, the RMBN enjoys considerable defense ability against the adversarial attacks.

In this article, we consider the problem of inferring the sign of a link based on known sign data in signed networks. Regarding this link sign prediction problem, signed directed graph neural networks (SDGNNs) provides the best prediction performance currently to the best of our knowledge. In this article, we propose a different link sign prediction architecture called subgraph encoding via linear optimization (SELO), which obtains overall leading prediction performances compared to the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization (LO) method. Comprehensive experiments are conducted on five real-world signed networks with area under curve (AUC), F1, micro-F1, and macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the five real-world networks and in all the four evaluation metrics.

In this article, we consider the problem of distributed game-theoretic learning in games with finite action sets. A timestamp-based inertial best-response dynamics is proposed for Nash equilibrium seeking by players over a communication network. We prove that if all players adhere to the dynamics, then the states of players will almost surely reach consensus and the joint action profile of players will be absorbed into a Nash equilibrium of the game. This convergence result is proven under the condition of weakly acyclic games and strongly connected networks. Furthermore, to encounter more general circumstances, such as games with graphical action sets, state-based games, and switching communication networks, several variants of the proposed dynamics and its convergent results are also developed. To demonstrate the validity and applicability, we apply the proposed timestamp-based learning dynamics to design distributed algorithms for solving some typical finite games, including the coordination games and congestion games.

In this article, we aim to answer the following question: What kind of games can guarantee convergence of the (full-information or partial-information, continuous-time or discrete-time) gradient play? To the best of our knowledge, current works on Nash equilibrium seeking are mainly established on the monotonicity condition. We introduce a concept called stability condition to continuous games, which includes the monotonicity condition as a special case. We prove that the stability condition is necessary and sufficient for convergence of gradient play. In detail, we show that, if the step size is fixed and within a given bound, the full-information and partial-information gradient play is guaranteed to converge to the Nash equilibrium in strongly stable games. If the step size is diminishing, then convergence of the gradient play can be obtained for strictly stable games. We present a game that is stable but not monotone to illustrate our theoretical developments.

This article addresses the problem of distributed Nash equilibrium seeking over networks for games with finite action sets. Gradient-like and consensus-based methods commonly used for continuous action spaces fail to work for this case. To this end, we propose a utility decoupling method to reformulate the original game into an augmented game, which preserves the Nash equilibrium and weakly acyclic property, yet enjoys a utility coupling network the same as the communication network. In this way, a variety of full-information game-theoretic learning dynamics for the augmented game turns into partial-information Nash equilibrium seeking dynamics for the original game. We proceed to apply the developed utility decoupling method to formulate three types of distributed Nash equilibrium seeking dynamics, including distributed best-response dynamics, distributed fictitious play, and distributed regret matching for weakly acyclic games. In the last, a typical color assignment game is utilized to empirically illustrate the validity and effectiveness of our approach.

In this article, an augmented game approach is proposed for the formulation and analysis of distributed learning dynamics in multiagent games. Through the design of the augmented game, the coupling structure of utility functions among all the players can be reformulated into an arbitrary undirected connected network while the Nash equilibria are preserved. In this case, any full-information game learning dynamics can be recast into a distributed form, and its convergence can be determined from the structure of the augmented game. We apply the proposed approach to generate both deterministic and stochastic distributed gradient play and obtain several negative convergent results about the distributed gradient play: 1) a Nash equilibrium is convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be not convergent under the distributed gradient play and, on the other side, 2) a Nash equilibrium is not convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be convergent under the distributed gradient play. In particular, we show that the variational stability structure (including monotonicity as a special case) of a game is not guaranteed to be preserved in its augmented game. These results provide a systematic methodology about how to formulate and then analyze the feasibility of distributed game learning dynamics.

The enclosing subgraph of a target link has been proved to be effective for prediction of potential links. However, it is still unclear what topological features of the subgraph play the key role in determining the existence of links. To give a possible answer to this question, in this paper, we propose a neural network based learning method for link prediction with only 1-hop neighborhood information. In detail, we extract the one-hop neighborhood of a target link as the enclosing subgraph, then encode the subgraph into different types of topological features, and lastly feed these features to train a fully connected neural network for link prediction. The experimental results show that our proposed learning method with the 1-hop neighborhood features could outperform those heuristic-based methods and achieve nearly equal performance to the state-of-the-art learning-based method WLNM and SEAL. Furthermore, it is observed that these features can be concatenated with attribute vectors to greatly promote the link prediction performance in attributed graphs. This indicates that the topological pattern within an enclosing subgraph, which determines the existence of a possible link, can be aggregated by some elementary subgraph features.

In this article, a consensus-based multipopulation game dynamics approach is proposed for distributed Nash equilibria seeking and optimization. The approach is fundamentally different from existing population dynamics from that: 1) the underlying communication network underlying the population game dynamics could be arbitrary undirected connected graph and more importantly 2) the proposed approach works in a distributed manner even when the objective functions of players are strongly coupled with each other. The proposed approach greatly extends the applicability of population game dynamics in distributed optimization and learning problems. A distributed constrained optimization problem and a traffic routing problem are utilized to illustrate the feasibility of the proposed multipopulation game dynamics approach.

In[1], the affiliation for Athanasios V. Vasilakos should be as follows:

Evolutionary games and population dynamics are finding increasing applications in design learning and control protocols for a variety of resource allocation problems. The implicit requirement for full communication has been the main limitation of the evolutionary game dynamic approach in engineering tasks with various information constraints. This article intends to build population games and dynamics with both static and dynamical graphical communication structures. To this end, we formulate a population game model with graphical strategy interactions and derive its corresponding population dynamics. In particular, we first introduce the concept of generalized Nash equilibria for population games with graphical strategy interactions, and establish the equivalence between the set of generalized Nash equilibria and the set of rest points of its distributed population dynamics. Furthermore, the conditions for convergence to generalized Nash equilibrium and particularly to Nash equilibrium are obtained for the distributed population dynamics with both static and dynamical graphical structures. These results provide a new approach to design distributed Nash equilibrium seeking algorithms for population games with both static and dynamical communication networks, and hence, expand the applicability of the population game dynamics in the design of learning and control protocols under distributed circumstances.

Pairwise-interaction graphical games have been widely used in the study and design of strategic interaction in multiagent systems. With regard to this issue, one entitative problem is actually to understand how the interaction structure of agents affects the strategy configuration of Nash equilibria. This paper intends to study the effect of interaction networks on Nash equilibria in pairwise-interaction graphical games. We first show that interaction networks may induce new strategy equilibria in pairwise-interaction graphical games and then provide graphical conditions for the existence of these network-induced equilibria. Furthermore, to determine Nash equilibria of pairwise-interaction graphical games, a graphical replicator dynamics model is formulated, and its connection with graphical games is established. In detail, it is shown that every Nash equilibrium of the graphical games corresponds to a fixed point of the graphical replicator dynamics and that every asymptotically stable fixed point of the graphical replicator dynamics corresponds to a strict pure Nash equilibrium of the graphical games. The obtained results are applied in understanding coordination in complex networks and determination of structural conflicts in signed graphs. This work may provide new insights into understanding and designing strategy equilibria and dynamics in games on networks.

Behavioral choice is ubiquitous across a wide range of interactive decision-making processes and a myriad of scientific disciplines. With regard to this issue, one entitative problem is actually to understand how collective social behaviors form and evolve among populations when they face a variety of conflict alternatives. In this paper, a selection-drift dynamic model is formulated to characterize the behavior imitation and exploration processes in social populations. Based on the proposed framework, several typical behavior evolution patterns, including behavioral flocking, collapse, and oscillation, are reproduced with different kinds of behavior networks. Interestingly, for the selection-drift dynamics on homogeneous symmetric behavior networks, we unveil the phase transition from behavioral flocking to collapse and derive the bifurcation diagram of the evolutionary stable behaviors in social behavior evolution. While via analyzing the survival conditions of the best behavior on heterogeneous symmetric behavior networks, we propose a selection-drift mechanism to guarantee consensus at the optimal behavior. Moreover, when the selection-drift dynamics on asymmetric behavior networks is simulated, it is shown that breaking the symmetry in behavior networks can induce various behavioral oscillations. These obtained results may shed new insights into understanding, detecting, and further controlling how social norm and cultural trends evolve.

Cooperative behaviors are widespread in biological and social populations. Yet the evolution of cooperation is still a puzzle in evolutionary theory. Recent researches have indicated that complex interactions among individuals may promote the evolution of cooperation under weak selection. However, the selection effect on cooperation has not been completely understood. This paper aims to characterize the impact of selection on the emergence of cooperation in evolutionary dynamics on complex networks. By theoretical analysis and numerical simulation, it is found that selection favors defection over cooperation for the birth-death process, while it may favor cooperation over defection for the death-birth process. Furthermore, we come to the condition on which cooperation is dominant over defection. In particular, there exists an optimal selection intensity which favors cooperation the best for the death-birth process. The obtained results indicate that appropriate selection can promote the evolution of cooperation in structured populations under some circumstances.

Strategy selection is a fundamental problem for the evolutionary game process in structured populations. This paper aims at investigating the strategy selection problem by introducing a continuous evolutionary game dynamics on complex networks. It is shown that the population preference for strategies keeps unchanged under random drift in the evolutionary process. However, because of selection, the population will favor one strategy over the other based on the population structure and game payoffs. In particular, for the prisoners dilemma game, our results show that the cooperation is never favored in complete networks. However, it is greatly promoted by cycle networks. The above results are consistent with those in the traditional discrete evolutionary game dynamics. It should be especially pointed out that the proposed framework provides a potential effective tool for analyzing and controlling the evolutionary process in populations.

It is well known that the evolutionary dynamics characterizes the process of competition and evolution of phenotypes and behaviors in a population. Intuitively, the individual with a higher fitness will have a higher survival probability, which should be reflected in the evolutionary dynamic model. However, due to the computational complexity of fixation probability, it is very difficult to prove the existence of this property in evolutionary dynamics on complex networks. This paper aims at providing a rigorously theoretical proof for the global existence of such property in the local evolutionary dynamics by using the coupling and splicing techniques. In particular, we also prove that the fixation probability is monotone increasing for the initial nodes set of mutants. Numerical simulations are also given to validate the proposed approaches.

It is well known that the selection of fixation probability is the fundamental problem for the evolutionary dynamics in structured populations. This paper aims to introduce a general approach for investigating the evolutionary dynamics in a class of structured populations. It includes the evolutionary game dynamics and constant selection dynamics with different asynchronous updating rules, such as ‘birth-death’, ‘voter model’, ‘death-birth’, and ‘imitation’. It should be pointed out that the proposed method provides an effective way to resolve the evolutionary dynamics on general graphs. In particular, it introduces a useful calculating tool to analyze various evolutionary dynamics on small order graphs.