Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether the agents have an incentive to unilaterally shift to an alternative learning algorithm. We capture such incentives as an algorithm’s rationality ratio, which is the ratio of the highest payoff an agent can obtain by unilaterally deviating from a learning algorithm to its payoff from following it. We define a learning algorithm to be c-rational if its rationality ratio is at most c irrespective of the game. We show that popular learning algorithms such as fictitious play and regret-matching are not c-rational for any constant ${mathrm { c}}geq 1$ . We also show that if an agent can only observe the actions of the other agents but not their payoffs, then there are games for which c-rational algorithms do not exist. We then propose a framework that can build upon any existing learning algorithm and establish, under mild assumptions, that our proposed algorithm is (i) c-rational for a given ${mathrm { c}}geq 1$ and (ii) the strategies of the agents converge to an equilibrium, with high probability, if all agents follow it.
{"title":"Rationality of Learning Algorithms in Repeated Normal-Form Games","authors":"Shivam Bajaj;Pranoy Das;Yevgeniy Vorobeychik;Vijay Gupta","doi":"10.1109/LCSYS.2024.3486631","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3486631","url":null,"abstract":"Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether the agents have an incentive to unilaterally shift to an alternative learning algorithm. We capture such incentives as an algorithm’s rationality ratio, which is the ratio of the highest payoff an agent can obtain by unilaterally deviating from a learning algorithm to its payoff from following it. We define a learning algorithm to be c-rational if its rationality ratio is at most c irrespective of the game. We show that popular learning algorithms such as fictitious play and regret-matching are not c-rational for any constant \u0000<inline-formula> <tex-math>${mathrm { c}}geq 1$ </tex-math></inline-formula>\u0000. We also show that if an agent can only observe the actions of the other agents but not their payoffs, then there are games for which c-rational algorithms do not exist. We then propose a framework that can build upon any existing learning algorithm and establish, under mild assumptions, that our proposed algorithm is (i) c-rational for a given \u0000<inline-formula> <tex-math>${mathrm { c}}geq 1$ </tex-math></inline-formula>\u0000 and (ii) the strategies of the agents converge to an equilibrium, with high probability, if all agents follow it.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1109/LCSYS.2024.3485963
Qingsong Liu;Li Ma
How to control the spread of disease is a challenging problem for human beings, and one of the main reasons is the diversity of disease transmission pathways. Besides, the existing literature shows that community’s opinion plays an important role in controlling the spread of disease. However, the influence of opinions on disease transmission with a waterborne pathogen is unclear. In this letter, we propose a nonlinear dynamic system to analyze the impact of the opinion on disease transmission with a waterborne pathogen and stubborn community. The criteria for determining the global and local stability of the proposed dynamic system are established, respectively. Based on the real data and Email-Eu-Core network, our proposed dynamic system is utilized to show that only the proportion of infected individuals decreased, but diseases and a waterborne pathogen did not disappear, which is completely different from the existing result that the disease disappeared when stubborn communities are introduced.
{"title":"Impact of Opinion on Disease Transmission With Waterborne Pathogen and Stubborn Community","authors":"Qingsong Liu;Li Ma","doi":"10.1109/LCSYS.2024.3485963","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3485963","url":null,"abstract":"How to control the spread of disease is a challenging problem for human beings, and one of the main reasons is the diversity of disease transmission pathways. Besides, the existing literature shows that community’s opinion plays an important role in controlling the spread of disease. However, the influence of opinions on disease transmission with a waterborne pathogen is unclear. In this letter, we propose a nonlinear dynamic system to analyze the impact of the opinion on disease transmission with a waterborne pathogen and stubborn community. The criteria for determining the global and local stability of the proposed dynamic system are established, respectively. Based on the real data and Email-Eu-Core network, our proposed dynamic system is utilized to show that only the proportion of infected individuals decreased, but diseases and a waterborne pathogen did not disappear, which is completely different from the existing result that the disease disappeared when stubborn communities are introduced.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1109/LCSYS.2024.3484635
Shantanu Singh;Nikolaos Bekiaris-Liberis
We perform various numerical tests to study the effect of (boundary) stenosis on blood flow stability, employing a detailed and accurate, second-order finite-volume scheme for numerically implementing a partial differential equation (PDE) model, using clinically realistic values for the artery’s parameters and the blood inflow. The model consists of a baseline $2times 2$ hetero-directional, nonlinear hyperbolic PDE system, in which, the stenosis’ effect is described by a pressure drop at the outlet of an arterial segment considered. We then study the stability properties (observed in our numerical tests) of a reference trajectory, corresponding to a given time-varying inflow (e.g., a periodic trajectory with period equal to the time interval between two consecutive heartbeats) and stenosis severity, deriving the respective linearized system and constructing a Lyapunov functional. Due to the fact that the linearized system is time varying, with time-varying parameters depending on the reference trajectories themselves (that, in turn, depend in an implicit manner on the stenosis degree), which cannot be derived analytically, we verify the Lyapunov-based stability conditions obtained, numerically. Both the numerical tests and the Lyapunov-based stability analysis show that a reference trajectory is asymptotically stable with a decay rate that decreases as the stenosis severity deteriorates.
{"title":"Numerical and Lyapunov-Based Investigation of the Effect of Stenosis on Blood Transport Stability Using a Control-Theoretic PDE Model of Cardiovascular Flow","authors":"Shantanu Singh;Nikolaos Bekiaris-Liberis","doi":"10.1109/LCSYS.2024.3484635","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3484635","url":null,"abstract":"We perform various numerical tests to study the effect of (boundary) stenosis on blood flow stability, employing a detailed and accurate, second-order finite-volume scheme for numerically implementing a partial differential equation (PDE) model, using clinically realistic values for the artery’s parameters and the blood inflow. The model consists of a baseline \u0000<inline-formula> <tex-math>$2times 2$ </tex-math></inline-formula>\u0000 hetero-directional, nonlinear hyperbolic PDE system, in which, the stenosis’ effect is described by a pressure drop at the outlet of an arterial segment considered. We then study the stability properties (observed in our numerical tests) of a reference trajectory, corresponding to a given time-varying inflow (e.g., a periodic trajectory with period equal to the time interval between two consecutive heartbeats) and stenosis severity, deriving the respective linearized system and constructing a Lyapunov functional. Due to the fact that the linearized system is time varying, with time-varying parameters depending on the reference trajectories themselves (that, in turn, depend in an implicit manner on the stenosis degree), which cannot be derived analytically, we verify the Lyapunov-based stability conditions obtained, numerically. Both the numerical tests and the Lyapunov-based stability analysis show that a reference trajectory is asymptotically stable with a decay rate that decreases as the stenosis severity deteriorates.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1109/LCSYS.2024.3482148
Anik Kumar Paul;Arun D. Mahindrakar;Rachel K. Kalaimani
This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm’s iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates’ function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy.
{"title":"Almost Sure Convergence and Non-Asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm","authors":"Anik Kumar Paul;Arun D. Mahindrakar;Rachel K. Kalaimani","doi":"10.1109/LCSYS.2024.3482148","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3482148","url":null,"abstract":"This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm’s iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates’ function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-14DOI: 10.1109/LCSYS.2024.3479275
Iryna Zabarianska;Anton V. Proskurnikov
This letter introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum $boldsymbol {xi }+boldsymbol {mathcal {O}}$ , where $boldsymbol {xi }$ is the agent’s current opinion and $boldsymbol {mathcal {O}}$ is the confidence set defining acceptable deviations. During each iteration, agents update their opinions by simultaneously averaging the trusted opinions. Unlike traditional HK systems, where $boldsymbol {mathcal {O}}$ is a ball in some norm, our model allows the confidence set to be non-convex and even unbounded. The new model, referred to as SCOD (Set-based Confidence Opinion Dynamics), can exhibit properties absent in the conventional HK model. Some solutions may converge to non-equilibrium points in the state space, while others oscillate periodically. These “pathologies” disappear if the set $boldsymbol {mathcal {O}}$ is symmetric and contains zero in its interior: similar to the usual HK model, the SCOD then converge in a finite number of iterations to one of the equilibrium points. The latter property is also preserved if one agent is “stubborn” and resists changing their opinion, yet still influences the others; however, two stubborn agents can lead to oscillations.
{"title":"Opinion Dynamics With Set-Based Confidence: Convergence Criteria and Periodic Solutions","authors":"Iryna Zabarianska;Anton V. Proskurnikov","doi":"10.1109/LCSYS.2024.3479275","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3479275","url":null,"abstract":"This letter introduces a new multidimensional extension of the Hegselmann-Krause (HK) opinion dynamics model, where opinion proximity is not determined by a norm or metric. Instead, each agent trusts opinions within the Minkowski sum \u0000<inline-formula> <tex-math>$boldsymbol {xi }+boldsymbol {mathcal {O}}$ </tex-math></inline-formula>\u0000, where \u0000<inline-formula> <tex-math>$boldsymbol {xi }$ </tex-math></inline-formula>\u0000 is the agent’s current opinion and \u0000<inline-formula> <tex-math>$boldsymbol {mathcal {O}}$ </tex-math></inline-formula>\u0000 is the confidence set defining acceptable deviations. During each iteration, agents update their opinions by simultaneously averaging the trusted opinions. Unlike traditional HK systems, where \u0000<inline-formula> <tex-math>$boldsymbol {mathcal {O}}$ </tex-math></inline-formula>\u0000 is a ball in some norm, our model allows the confidence set to be non-convex and even unbounded. The new model, referred to as SCOD (Set-based Confidence Opinion Dynamics), can exhibit properties absent in the conventional HK model. Some solutions may converge to non-equilibrium points in the state space, while others oscillate periodically. These “pathologies” disappear if the set \u0000<inline-formula> <tex-math>$boldsymbol {mathcal {O}}$ </tex-math></inline-formula>\u0000 is symmetric and contains zero in its interior: similar to the usual HK model, the SCOD then converge in a finite number of iterations to one of the equilibrium points. The latter property is also preserved if one agent is “stubborn” and resists changing their opinion, yet still influences the others; however, two stubborn agents can lead to oscillations.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10715999","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1109/LCSYS.2024.3478272
Maxwell Fitzsimmons;Jun Liu
A contraction metric defines a differential Lyapunov-like function that robustly captures the convergence between trajectories. In this letter, we investigate the use of neural networks for computing verifiable contraction metrics. We first prove the existence of a smooth neural network contraction metric within the domain of attraction of an exponentially stable equilibrium point. We then focus on the computation of a neural network contraction metric over a compact invariant set within the domain of attraction certified by a physics-informed neural network Lyapunov function. We consider both partial differential inequality (PDI) and equation (PDE) losses for computation. We show that sufficiently accurate neural approximate solutions to the PDI and PDE are guaranteed to be a contraction metric under mild technical assumptions. We rigorously verify the computed neural network contraction metric using a satisfiability modulo theories solver. Through numerical examples, we demonstrate that the proposed approach outperforms traditional semidefinite programming methods for finding sum-of-squares polynomial contraction metrics.
{"title":"Computation and Formal Verification of Neural Network Contraction Metrics","authors":"Maxwell Fitzsimmons;Jun Liu","doi":"10.1109/LCSYS.2024.3478272","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3478272","url":null,"abstract":"A contraction metric defines a differential Lyapunov-like function that robustly captures the convergence between trajectories. In this letter, we investigate the use of neural networks for computing verifiable contraction metrics. We first prove the existence of a smooth neural network contraction metric within the domain of attraction of an exponentially stable equilibrium point. We then focus on the computation of a neural network contraction metric over a compact invariant set within the domain of attraction certified by a physics-informed neural network Lyapunov function. We consider both partial differential inequality (PDI) and equation (PDE) losses for computation. We show that sufficiently accurate neural approximate solutions to the PDI and PDE are guaranteed to be a contraction metric under mild technical assumptions. We rigorously verify the computed neural network contraction metric using a satisfiability modulo theories solver. Through numerical examples, we demonstrate that the proposed approach outperforms traditional semidefinite programming methods for finding sum-of-squares polynomial contraction metrics.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142452689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-07DOI: 10.1109/LCSYS.2024.3475886
Luca Ballotta;Geethu Joseph;Irawati Rahul Thete
This letter considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization.
{"title":"Pointwise-Sparse Actuator Scheduling for Linear Systems With Controllability Guarantee","authors":"Luca Ballotta;Geethu Joseph;Irawati Rahul Thete","doi":"10.1109/LCSYS.2024.3475886","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3475886","url":null,"abstract":"This letter considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This letter introduces a novel fully distributed estimation scheme for nonlinear continuous-time dynamics over directed and strongly connected graphs. Leveraging on the assumption of local negativizability, the proposed approach performs the estimation of the interdependent subsystems of a cyber-physical system, despite the presence of nonlinear dependencies on the dynamics. This transforms the intricate task of nonlinear state estimation by each agent into more manageable local negativizability problems for the design of the estimation gains. A pivotal aspect of the approach is that each agent should be aware of an upper bound on the Lipschitz constant of the overall nonlinear function that characterizes the dynamics. To face this issue, we developed a novel distributed methodology for the estimation of the global Lipschitz constant, starting from the local observations of the system’s nonlinearities. The effectiveness of the proposed scheme is numerically demonstrated through simulations.
{"title":"Negativizability for Nonlinear Estimation in Cyber–Physical Systems","authors":"Camilla Fioravanti;Stefano Panzieri;Gabriele Oliva","doi":"10.1109/LCSYS.2024.3473789","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3473789","url":null,"abstract":"This letter introduces a novel fully distributed estimation scheme for nonlinear continuous-time dynamics over directed and strongly connected graphs. Leveraging on the assumption of local negativizability, the proposed approach performs the estimation of the interdependent subsystems of a cyber-physical system, despite the presence of nonlinear dependencies on the dynamics. This transforms the intricate task of nonlinear state estimation by each agent into more manageable local negativizability problems for the design of the estimation gains. A pivotal aspect of the approach is that each agent should be aware of an upper bound on the Lipschitz constant of the overall nonlinear function that characterizes the dynamics. To face this issue, we developed a novel distributed methodology for the estimation of the global Lipschitz constant, starting from the local observations of the system’s nonlinearities. The effectiveness of the proposed scheme is numerically demonstrated through simulations.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10706085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1109/LCSYS.2024.3474057
Kaiyun Xie;Junlin Xiong
This letter focuses on designing approximate Nash strategies for the two-person zero-sum Markov game. Using the receding horizon method, the $epsilon $ -optimal strategies are designed to approximate Nash strategies by executing finite Gauss-Seidel iterations. The relationship between the approximation value of $epsilon $ and the number of iterations is also analyzed. Additionally, the $epsilon $ -optimal strategies are designed for two scenarios with imprecise parameters. For scenarios with imprecise values, the value of $epsilon $ is determined based on the errors between imprecise and iteration values. It provides a theoretical basis for efficiently designing $epsilon $ -optimal strategies using heuristic algorithms or approximate dynamic programming. For scenarios with imprecise transition probabilities, the value of $epsilon $ is determined based on the errors between the estimated and practical transition probabilities. It enables the use of pattern recognition technology or other methods to estimate practical transition probabilities for designing $epsilon $ -optimal strategies.
{"title":"The Design of ϵ-Optimal Strategy for Two-Person Zero-Sum Markov Games","authors":"Kaiyun Xie;Junlin Xiong","doi":"10.1109/LCSYS.2024.3474057","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3474057","url":null,"abstract":"This letter focuses on designing approximate Nash strategies for the two-person zero-sum Markov game. Using the receding horizon method, the \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000-optimal strategies are designed to approximate Nash strategies by executing finite Gauss-Seidel iterations. The relationship between the approximation value of \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000 and the number of iterations is also analyzed. Additionally, the \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000-optimal strategies are designed for two scenarios with imprecise parameters. For scenarios with imprecise values, the value of \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000 is determined based on the errors between imprecise and iteration values. It provides a theoretical basis for efficiently designing \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000-optimal strategies using heuristic algorithms or approximate dynamic programming. For scenarios with imprecise transition probabilities, the value of \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000 is determined based on the errors between the estimated and practical transition probabilities. It enables the use of pattern recognition technology or other methods to estimate practical transition probabilities for designing \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000-optimal strategies.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1109/LCSYS.2024.3472495
Roberta Raineri;Chiara Ravazzi;Giacomo Como;Fabio Fagnani
The wide spread of on-line social networks poses new challenges in information environment and cybersecurity. A key issue is detecting stubborn behaviors to identify leaders and influencers for marketing purposes, or extremists and automatic bots as potential threats. Existing literature typically relies on known network topology and extensive centrality measures computation. However, the size of social networks and their often unknown structure could make social influence computation impractical. We propose a new approach based on opinion dynamics to estimate stubborn agents from data. We consider a DeGroot model in which regular agents adjust their opinions as a linear combination of their neighbors’ opinions, whereas stubborn agents keep their opinions constant over time. We formulate the stubborn nodes identification and their influence estimation problems as a low-rank approximation problem. We then propose an interpolative decomposition algorithm for their solution. We determine sufficient conditions on the model parameters to ensure the algorithm’s resilience to noisy observations. Finally, we corroborate our theoretical analysis through numerical results.
{"title":"Detecting Stubborn Behaviors in Influence Networks: A Model-Based Approach for Resilient Analysis","authors":"Roberta Raineri;Chiara Ravazzi;Giacomo Como;Fabio Fagnani","doi":"10.1109/LCSYS.2024.3472495","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3472495","url":null,"abstract":"The wide spread of on-line social networks poses new challenges in information environment and cybersecurity. A key issue is detecting stubborn behaviors to identify leaders and influencers for marketing purposes, or extremists and automatic bots as potential threats. Existing literature typically relies on known network topology and extensive centrality measures computation. However, the size of social networks and their often unknown structure could make social influence computation impractical. We propose a new approach based on opinion dynamics to estimate stubborn agents from data. We consider a DeGroot model in which regular agents adjust their opinions as a linear combination of their neighbors’ opinions, whereas stubborn agents keep their opinions constant over time. We formulate the stubborn nodes identification and their influence estimation problems as a low-rank approximation problem. We then propose an interpolative decomposition algorithm for their solution. We determine sufficient conditions on the model parameters to ensure the algorithm’s resilience to noisy observations. Finally, we corroborate our theoretical analysis through numerical results.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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