Byzantine resilience is essential in federated learning (FL) to safeguard model training from malicious or faulty participants. However, existing Byzantine-resilient methods struggle when faced with heavy-tailed gradient noise, a common challenge in heterogeneous environments. In this work, we propose a Byzantine-resilient FL framework specifically designed to handle both heterogeneity and heavy-tailed noise. Our approach builds on robust distributed stochastic heavy-ball optimization, incorporating update normalization and gradient/momentum clipping to mitigate the effects of heavy-tailed noise. We establish the first high-probability convergence guarantees for Byzantine-resilient FL under these conditions, showing that our algorithms achieve optimal Byzantine resilience and align with known lower bounds. Additionally, we introduce an efficient variant of the nearest neighbor mixing technique, leveraging random projections to significantly reduce computational costs in high-dimensional settings. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate that our methods outperform existing approaches in robustness against both Byzantine failures and heavy-tailed noise.

Spectrum sharing is a key enabler for 5G/6G. We model decentralized spectrum access as a noncooperative, stochastic, imperfect-information extensive-form game and show that running standard Counterfactual Regret Minimization (CFR) independently at each user can exhibitpersistent cyclingrather than converging to a stable equilibrium. We provide a constructive multi-player example and a mapping analysis explaining why the induced regret-matching update need not be contractive in general multi-player, non-zero-sum settings. To address this, we propose CFR-M2, a lightweightregret-mixingscheme that periodically aggregates a small amount ofcumulative regret(not policy parameters) across users at a configurable communication interval. Our analysis shows that inserting an infrequent regret-consensus step over any connected communication graph preserves no-(counterfactual)-regret whilecontracting inter-agent disagreement in regrets. Consequently, the C´esaro-averaged play converges to an ε–extensive-form coarse correlated equilibrium (EFCCE) with ε=Õ(1/√T)+O(RMAXTCOMM/(1-ρ)T) where ρ is the second-largest eigenvalue modulus of the mixing matrix. Under additional structure (e.g., a strongly monotone pseudo-gradient or a strongly convex potential), the EFCCE collapses to a unique Nash equilibrium. Experiments on synthetic networks and a 5G Dynamic Spectrum Sharing (DSS) scenario (WINNER II channel model and practical parameter settings) show that CFR-M2improves convergence stability and system reward over CFR and several learning/game-theoretic baselines, while requiring onlyinfrequentcommunications.

With the advancements of artificial intelligence (AI), emerging scenarios involving close collaboration between AI and other unknown agents are becoming increasingly common. This requires sometimes training AI agents to collaborate with unknown agents in the absence of a reward function -- which may be unavailable to the AI agents or even undefined by the unknown agents themselves -- thus posing news challenges to existing learning algorithms that often require knowing the shared reward. In this paper, we show that effective teaming with unknown agents can be achieved in the absence of a reward function, through actively modeling other unknown agents and reasoning about their latent rewards from available interaction/observation history. In particular, we propose a novel framework that leverages a kernel density Bayesian inverse learning method for active reward/goal inference and prove that multi-agent reinforcement learning guided by the inferred reward signals can converge to an optimal policy teaming with unknown agents. The result enables us to develop an adaptive policy update strategy, through the use of a family of pre-trained, goal-conditioned policies, further eliminating the need for online retraining. The proposed solution is evaluated using a wide range of diverse unknown agents of latent and even non-stationary reward. Our solution significantly increases the teaming performance between AI and unknown agents in the absence of reward.

We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: \textbf{(i)} inaccurate convergence error rate due to overlooking gradient variance in the saddle point escape analysis, and \textbf{(ii)} dependence on auxiliary private model selection procedures for identifying DP-SOSP, which can significantly impair utility, particularly in distributed settings. To address these issues, we propose a generic perturbed stochastic gradient descent (PSGD) framework built upon Gaussian noise injection and general gradient oracles. A core innovation of our framework is using model drift distance to determine whether PSGD escapes saddle points, ensuring convergence to approximate local minima without relying on second-order information or additional DP-SOSP identification. By leveraging the adaptive DP-SPIDER estimator as a specific gradient oracle, we develop a new DP algorithm that rectifies the convergence error rates reported in prior work. We further extend this algorithm to distributed learning with heterogeneous data, providing the first formal guarantees for finding DP-SOSP in such settings. Our analysis also highlights the detrimental impacts of private selection procedures in distributed learning under high-dimensional models, underscoring the practical benefits of our design. Numerical experiments on real-world datasets validate the efficacy of our approach.

The openness of wireless networks opens the door to Byzantine attacks on the physical channels, making the communications unreliable and resulting in more challenges in achieving consensus among mobile devices. To address this issue, this paper studies the Byzantine-fault-tolerant (BFT) consensus problem based on an unreliable Byzantine communication model. Different from the previous works requiring stable communications between the honest nodes, considering the unreliable communication makes our problem more realistic but also harder. Based on the unreliable communication model, we first implement a BFT abstract MAC (absMAC) layer with a distributed and randomized multi-channel communication algorithm. In the implemented absMAC layer, its acknowledgement and progress operations can be completed within$O\left ({{\frac {kn}{k-f}\log n}}\right)$and$O\left ({{\frac {k}{k-f}\log n}}\right)$rounds, respectively. n, f, and k are the numbers of nodes, Byzantine nodes, and channels, respectively. With the implemented absMAC layer, an efficient and elegant BFT consensus algorithm is designed, which can solve the binary consensus problem within$O\left ({{\frac {kn}{k-f}\log n}}\right) ^{^{^{^{}}}}$rounds in expectation. Even though a series of works have discussed how to achieve consensus with a specific absMAC layer provided, to the best of our knowledge, this paper is the first one that implements a BFT absMAC layer.

Many emerging applications in edge computing require processing of huge volumes of data generated by end devices, using the freshest available information. In this paper, we address the distributed optimization of multi-user long-term average Age-of-Information (AoI) objectives in edge networks that use NOMA transmission. This poses a challenge of non-convex online optimization, which in existing work often requires either decision making in a combinatorial space or a global view of entire network states. To overcome this challenge, we propose a reinforcement learning-based framework that adopts a novel hierarchical decomposition of decision making. Specifically, we propose three different types of distributed agents to learn with respect to efficiency of AoI scheduling, fairness of AoI scheduling, as well as a high-level policy balancing these potentially conflicting design objectives. Not only does the proposed decomposition improve learning performance due to disentanglement of different design objectives/rewards, but it also enables the algorithm to learn the best policy while also learning the explanations – as actions can be directly compared in terms of the design objectives. Our evaluations show that the proposed algorithm improves the long-term average AoI by$200\%{-}300\%$and 400% compared to prior works with NOMA and the optimal solution without NOMA, respectively.

As an integration of digital twin and edge computing, the digital twin edge networks (DITENs) have been proposed in recent years to fill the gap between physical edge networks and digital systems. Meanwhile, the multi-access wireless environments in edge computing make it hard to provide ultra-reliable and low-latency communications for digital twin, especially when the jamming attacks can be launched by the adversaries. This paper studies the jamming-resilient physical-to-virtual communication (PTVC) problem in DITENs despite strong cooperative jamming. Note that the previous jamming models mainly focus on the jamming behaviors from individual adversaries and are restricted by the energy budget limitation and uniform jamming assumption. In this paper, we consider a more comprehensive jamming model, in whichfadversaries can cooperatively launch their jamming attacks in totallykwireless channels with unlimited power budget and non-uniform jamming signals. Then, based on the new proposed$(k,f)$-cooperative jamming model, we show that$k\gt f$is the necessary and also sufficient condition to solve the PTVC problem. On one hand, we prove that the PTVC problem is insoluble when$f\leq k$; on the other hand, two distributed algorithms are given as the solutions of the PTVC problem amongnphysical objectives and one sink node when$k\gt f$, the time complexity of which are$O\left ({{\frac {n \log n}{k (\log k-\log f)}}}\right)$and$O\left ({{\frac {n \log n}{\log k-\log f}}}\right)$based on the communication modes with/without acknowledgement, respectively. Both of the theoretical results and empirical simulations are conducted to show the resilience of our algorithms despite such a strong cooperative jamming model.

In this paper, we propose Byzantine-Robust Decentralized Federated Reinforcement Learning (BR-DeFedRL), an innovative framework that effectively combats the harmful influence of Byzantine agents by adaptively adjusting communication weights, thereby significantly enhancing the robustness of the learning system. By leveraging decentralized learning, our approach eliminates the dependence on a central server. Striking a harmonious balance between communication round count and sample complexity, BR-DeFedRL achieves efficient convergence with a rate of $\mathcal{O}\left( {\frac{1}{{TN}}} \right)$, where T denotes the communication rounds and N represents the local steps related to variance reduction. Notably, each agent attains an ϵ-approximation with a state-of-the-art sample complexity of $\mathcal{O}\left( {\frac{1}{{\varepsilon N}} + \frac{1}{\varepsilon }} \right)$. Extensive experimental validations further affirm the efficacy of BR-DeFedRL, making it a promising and practical solution for Byzantine-robust decentralized federated reinforcement learning.

This paper addresses the problem of reliable communications for cooperative learning on Internet-of-Vehicles, where a large amount of data from users and services needs to be processed. Previous works have proposed various cooperative learning schemes, but they often assume that the communications between vehicles are reliable, without considering how to achieve this in an Internet-of-Vehicles network. This paper is the first one that implements an abstract MAC layer using a distributed deep reinforcement learning scheme, which can directly meet the reliable communication requirements of cooperative learning in previous works. Our abstract MAC layer performs two operations:acknowledgement, which makes sure that all vehicles can successfully broadcast their messages to all of their neighbors, andprogress, which ensures that each vehicle can receive at least one message from its neighbors. These operations facilitate vehicles to exchange and update their training models in a cooperative learning service. Our simulation results show the efficiency and fairness of our deep reinforcement learning abstract MAC layer.

k-terminal network reliability is the probability that k terminal vertices are connected given that edges in the network fail independently while vertices do not fail. It depends on the distribution of these terminal vertices as well as network topology. The problem of computing k-terminal reliability is NP-hard. Previous literature mainly focus on designing efficient algorithms to compute it in different graphs, but are lacking in the analysis for optimal distribution of k terminal vertices in sparse graphs, within which those with n nodes and m edges, where m ≤ n + 1, are most basic classes. Hence, it is of great significance to investigate the optimal distribution of terminal vertices in these classes of graphs before considering general cases. In this paper, we prove that k-terminal network reliability obtains the maximum if k terminal vertices induce a connected subgraph. Further, we give equations of maximum reliability for all possible graphs in the above classes. The experiments illustrate the variation, with several parameters and according to our theoretical results, of maximal k-terminal reliability, and provide observations for graphs with any number of edges.

Multistate two-terminal reliability is the probability that d units of flow can be transmitted from the source nodes to the sink node t. It is an important index fora flow network, and its value is based on minpaths or mincuts. However, the enumeration of all minpaths is not feasible in large networks. Hence, designing an approximation algorithm is valuable for the reliability of multistate flow networks. In this paper, we model a multistate flow network as an acyclic directed graph and find that the contribution of minpaths to the reliability changes with their lengths, so we consider the approximation solution of multistate two-terminal reliability by constraining diameter of the network. Furthermore, we give a sufficient and necessary condition to detect irrelevant arcs and propose an approximation algorithm by controlling the value of diameter constraint. In the meantime, the reliability with diameter constraint is also a parameter to partially reflect the performance of network. The experiments demonstrate the effectiveness and efficiency of the algorithm.

A cyber-physical system consists of two interacting networks, where the cyber network overlays the physical network. Due to the interdependence, node failures in one network may lead to failures of the other network and result in cascading failures of the whole system. One of the reasons for this phenomena is attributed to the connectivity of the interdependent system, which hinges heavily on the operation probability (or equivalently reliability) of networks in the light of node reliability. In this paper, we present the model of k-reliability, define cascading failures based on k-reliability, and propose an algorithm to calculate k-reliability for estimation of potential cascading failures. The proposed k-reliability, defined as the probability that at least k surviving nodes span an operating subnetwork, explains the operation probability of the system and reflects the connectivity of nodes in networks. In particular, we find that the network with regular interlink allocation strategy is homogeneous to the network with maximum k-reliability in class of graphs with 2n nodes and 2d edges when the information of intratopology is unknown. That is, regardless of the information of each individual network, the strategy that all nodes in the system are allotted the same number of bidirectional interlinks yields better performance on k- reliability than all other possible strategies both analytically and experimentally.