In this paper, a consensus algorithm is proposed for interacting multi-agents, which can be modeled as simple Mechanical Control Systems (MCS) evolving on a general Lie group. The standard Laplacian flow consensus algorithm for double integrator systems evolving on Euclidean spaces is extended to a general Lie group. A tracking error function is defined on a general smooth manifold for measuring the error between the configurations of two interacting agents. The stability of the desired consensus equilibrium is proved using a generalized version of Lyapunov theory and LaSalle's invariance principle applicable for systems evolving on a smooth manifold. The proposed consensus control input requires only the configuration information of the neighboring agents and does not require their velocities and inertia tensors. The design of tracking error function and consensus control inputs are demonstrated through an application of attitude consensus problem for multiple communicating rigid bodies. The consensus algorithm is numerically validated by demonstrating the attitude consensus problem.

Inconsistent outputs and hallucinations from large language models (LLMs) are major obstacles to reliable AI systems. When different proprietary reasoning models (RMs), such as those by OpenAI, Google, Anthropic, DeepSeek, and xAI, are given the same complex request, they often produce divergent results due to variations in training and inference. This paper proposes a novel consensus mechanism, inspired by distributed ledger technology, to validate and converge these outputs, treating each RM as a black-box peer. Building on the Hashgraph consensus algorithm, our approach employs gossip-about-gossip communication and virtual voting to achieve agreement among an ensemble of RMs. We present an architectural design for a prototype system in which RMs iteratively exchange and update their answers, using information from each round to improve accuracy and confidence in subsequent rounds. This approach goes beyond simple majority voting by incorporating the knowledge and cross-verification content of every model. We justify the feasibility of this Hashgraph-inspired consensus for AI ensembles and outline its advantages over traditional ensembling techniques in reducing nonfactual outputs. Preliminary considerations for implementation, evaluation criteria for convergence and accuracy, and potential challenges are discussed. The proposed mechanism demonstrates a promising direction for multi-agent AI systems to self-validate and deliver high-fidelity responses in complex tasks.

In this paper, the authors studied the problem of multitask reinforcement learning (MTRL), and propose several optimization techniques to alleviate the scalability issues observed in other methods, especially when the number of tasks or trajectories is large. Specifically, they rely on consensus algorithms to scale up MTRL algorithms and avoid the issues that exist in centralized solution methods. Furthermore, they show how MTRL algorithms can be improved over state-of-the-art benchmarks by considering the problem from a variational inference perspective, and then propose a novel distributed solver for MTRL with quadratic convergence guarantees. In general, this work is tackling some important problems in the increasingly popular domain of multi-task RL. Using the variational perspective of RL, the problem of MTRL can be cast as a variational inference problem, and policy search can be done through the minimization of the ELBO loss. To alternate the updates on variational parameters and the policy parameters, the authors also propose using EM based approaches, which is very reasonable.

Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems are inherently vulnerable to disruption. To develop a resilient consensus approach, inspiration is taken from the study of social systems and their dynamics; specifically, the Deffuant Model. A dynamic algorithm is presented enabling efficient consensus to be reached with an unknown number of disruptors present within a multi-agent system. By inverting typical social tolerance, agents filter out extremist non-standard opinions that would drive them away from consensus. This approach allows distributed systems to deal with unknown disruptions, without knowledge of the network topology or the numbers and behaviours of the disruptors. A disruptor-agnostic algorithm is particularly suitable to real-world applications where this information is typically unknown. Faster and tighter convergence can be achieved across a range of scenarios with the social dynamics inspired algorithm, compared with standard Mean-Subsequence-Reduced-type methods.

With the rapid development of machine learning and a growing concern for data privacy, federated learning has become a focal point of attention. However, attacks on model parameters and a lack of incentive mechanisms hinder the effectiveness of federated learning. Therefore, we propose A Privacy Protected Blockchain-based Federated Learning Model (PPBFL) to enhance the security of federated learning and encourage active participation of nodes in model training. Blockchain technology ensures the integrity of model parameters stored in the InterPlanetary File System (IPFS), providing protection against tampering. Within the blockchain, we introduce a Proof of Training Work (PoTW) consensus algorithm tailored for federated learning, aiming to incentive training nodes. This algorithm rewards nodes with greater computational power, promoting increased participation and effort in the federated learning process. A novel adaptive differential privacy algorithm is simultaneously applied to local and global models. This safeguards the privacy of local data at training clients, preventing malicious nodes from launching inference attacks. Additionally, it enhances the security of the global model, preventing potential security degradation resulting from the combination of numerous local models. The possibility of security degradation is derived from the composition theorem. By introducing reverse noise in the global model, a zero-bias estimate of differential privacy noise between local and global models is achieved. Furthermore, we propose a new mix transactions mechanism utilizing ring signature technology to better protect the identity privacy of local training clients. Security analysis and experimental results demonstrate that PPBFL, compared to baseline methods, not only exhibits superior model performance but also achieves higher security.

Among ensemble clustering methods, Evidence Accumulation Clustering is one of the simplest technics. In this approach, a co-association (CA) matrix representing the co-clustering frequency is built and then clustered to extract consensus clusters. Compared to other approaches, this one is simple as there is no need to find matches between clusters obtained from two different partitionings. Nevertheless, this method suffers from computational issues, as it requires to compute and store a matrix of size n x n, where n is the number of items. Due to the quadratic cost, this approach is reserved for small datasets. This work describes a trick which mimic the behavior of average linkage clustering. We found a way of computing efficiently the density of a partitioning, reducing the cost from a quadratic to linear complexity. Additionally, we proved that the k-means maximizes naturally the density. We performed experiments on several benchmark datasets where we compared the k-means and the bisecting version to other state-of-the-art consensus algorithms. The k-means results are comparable to the best state of the art in terms of NMI while keeping the computational cost low. Additionally, the k-means led to the best results in terms of density. These results provide evidence that consensus clustering can be solved with simple algorithms.

With the increasing importance of machine learning, the privacy and security of training data have become critical. Federated learning, which stores data in distributed nodes and shares only model parameters, has gained significant attention for addressing this concern. However, a challenge arises in federated learning due to the Byzantine Attack Problem, where malicious local models can compromise the global model's performance during aggregation. This article proposes the Blockchain-based Byzantine-Robust Federated Learning (BRLF) model that combines federated learning with blockchain technology. This integration enables traceability of malicious models and provides incentives for locally trained clients. Our approach involves selecting the aggregation node based on Pearson's correlation coefficient, and we perform spectral clustering and calculate the average gradient within each cluster, validating its accuracy using local dataset of the aggregation nodes. Experimental results on public datasets demonstrate the superior byzantine robustness of our secure aggregation algorithm compared to other baseline byzantine robust aggregation methods, and proved our proposed model effectiveness in addressing the resource consumption problem.

This paper considers solving distributed convex optimization problems in peer-to-peer multi-agent networks. The network is assumed to be synchronous and connected. By using the proportional-integral (PI) control strategy, various algorithms with fixed stepsize have been developed. The earliest among them is the PI consensus algorithm. Using Lyapunov theory, we guarantee exponential convergence of the PI consensus algorithm for restricted strongly convex functions with rate-matching discretization, without requiring convexity of individual local cost functions, for the first time. In order to accelerate the PI consensus algorithm, we incorporate local pre-conditioning in the form of constant positive definite matrices and numerically validate its efficiency compared to the prominent distributed convex optimization algorithms. Unlike classical pre-conditioning, where only the gradients are multiplied by a pre-conditioner, the proposed pre-conditioning modifies both the gradients and the consensus terms, thereby controlling the effect of the communication graph between the agents on the PI consensus algorithm.

A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network without imposing any differentiability assumptions. Firstly, a tractable approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints and restricting the right-hand side of the constraints with a proper positive parameter, which will be iteratively solved by a random-fixed projection algorithm. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed feasibility. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and populating the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time convergence of the distributed optimization, a distributed termination algorithm is developed based on uniformly local consensus and zeroth-order optimality under uniformly strongly connected graphs. Fourthly, it is proved that the cutting-surface consensus approach converges within a finite number of iterations. Finally, the effectiveness of the approach is illustrated through a numerical example.

In this paper, we introduce a novel adaptation of the Raft consensus algorithm for achieving emergent formation control in multi-agent systems with a single integrator dynamics. This strategy, dubbed "Rafting," enables robust cooperation between distributed nodes, thereby facilitating the achievement of desired geometric configurations. Our framework takes advantage of the Raft algorithm's inherent fault tolerance and strong consistency guarantees to extend its applicability to distributed formation control tasks. Following the introduction of a decentralized mechanism for aggregating agent states, a synchronization protocol for information exchange and consensus formation is proposed. The Raft consensus algorithm combines leader election, log replication, and state machine application to steer agents toward a common, collaborative goal. A series of detailed simulations validate the efficacy and robustness of our method under various conditions, including partial network failures and disturbances. The outcomes demonstrate the algorithm's potential and open up new possibilities in swarm robotics, autonomous transportation, and distributed computation. The implementation of the algorithms presented in this paper is available at https://github.com/abbas-tari/raft.git.