We consider the problem of distributed convergence to a Nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions, corrupted with additive measurement noise. Exact analytical forms and/or parameters of the cost functions, as well as the current actions of the players may be unknown. Additionally, the players' actions are subject to linear dynamic constraints. We propose an algorithm based on discrete-time stochastic extremum seeking using sinusoidal perturbations and prove its almost sure convergence to a Nash equilibrium. We show how the proposed algorithm can be applied to solving coordination problems in mobile sensor networks, where motion dynamics of the players can be modeled as: 1) single integrators (velocity-actuated vehicles), 2) double integrators (force-actuated vehicles), and 3) unicycles (a kinematic model with nonholonomic constraints). Examples are given in which the cost functions are selected such that the problems of connectivity control, formation control, rendezvous and coverage control are solved in an adaptive and distributed way. The methodology is illustrated through simulations.

In this paper, an algorithm for decentralized multi-agent estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. An analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of getting local measurements and implementing exchange of inter-agent messages. In the case of non-vanishing gains in the stochastic approximation algorithms, an asymptotic estimation error covariance matrix bound is defined as the solution of a Lyapunov-like matrix equation. In the case of asymptotically vanishing gains, the mean-square convergence is proved and the rate of convergence estimated. In the discussion, the problem of additive communication noise is treated in a methodologically consistent way. It is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence. Some simulation results illustrate the obtained theoretical results.

Recent advances in online payment technologies combined with the impact of the COVID-19 global pandemic has led to a significant escalation in the number of online transactions and credit card payments being executed every day. Naturally, there has also been an escalation in credit card frauds, which is having a significant impact on the banking institutions, corporations that issue credit cards, and finally, the vendors and merchants. Consequently, there is an urgent need to implement and establish proper mechanisms that can secure the integrity of online card transactions. The research presented in this paper proposes a hybrid machine learning and swarm metaheuristic approach to address the challenge of credit card fraud detection. The novel, enhanced firefly algorithm, named group search firefly algorithm, was devised and then used to a tune support vector machine, an extreme learning machine, and extreme gradient-boosting machine learning models. Boosted models were tested on the real-world credit card fraud detection dataset, gathered from the transactions of the European credit card users. The original dataset is highly imbalanced; to further analyze the performance of tuned machine learning models, in the second experiment performed for the purpose of this research, the dataset has been expanded by utilizing the synthetic minority over-sampling approach. The performance of the proposed group search firefly metaheuristic was compared with other recent state-of-the-art approaches. Standard machine learning performance indicators have been used for the evaluation, such as the accuracy of the classifier, recall, precision, and area under the curve. The experimental findings clearly demonstrate that the models tuned by the proposed algorithm obtained superior results in comparison to other models hybridized with competitor metaheuristics.