Pub Date : 2023-11-20DOI: 10.1109/JSAIT.2023.3334692
Shubham Aggarwal;Muhammad Aneeq uz Zaman;Melih Bastopcu;Tamer Başar
In this paper, we study a multi-agent game between $N$ agents, which solve a consensus problem, and receive state information through a wireless network, that is controlled by a Base station (BS). Due to a hard-bandwidth constraint, the BS can concurrently connect at most $R_{d} < N$ agents over the network. This causes an intermittency in the agents’ state information, necessitating state estimation based on each agent’s information history. Under standard assumptions on the information structure, we separate each agent’s estimation and control problems. The BS aims to find the optimum scheduling policy that minimizes a weighted age of information based performance metric, subject to the hard-bandwidth constraint. We first relax the hard constraint to a soft update-rate constraint and compute an optimal policy for the relaxed problem by reformulating it into an MDP. This then inspires a sub-optimal policy for the bandwidth constrained problem, which is shown to approach the optimal policy as $N rightarrow infty $ . Next, we solve the consensus problem using the mean-field game framework. By explicitly constructing the mean-field system, we prove the existence of a unique mean-field equilibrium. Consequently, we show that the equilibrium policies obtained constitute an $epsilon $ –Nash equilibrium for the finite-agent system.
{"title":"Weighted Age of Information-Based Scheduling for Large Population Games on Networks","authors":"Shubham Aggarwal;Muhammad Aneeq uz Zaman;Melih Bastopcu;Tamer Başar","doi":"10.1109/JSAIT.2023.3334692","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3334692","url":null,"abstract":"In this paper, we study a multi-agent game between \u0000<inline-formula> <tex-math>$N$ </tex-math></inline-formula>\u0000 agents, which solve a consensus problem, and receive state information through a wireless network, that is controlled by a Base station (BS). Due to a hard-bandwidth constraint, the BS can concurrently connect at most \u0000<inline-formula> <tex-math>$R_{d} < N$ </tex-math></inline-formula>\u0000 agents over the network. This causes an intermittency in the agents’ state information, necessitating state estimation based on each agent’s information history. Under standard assumptions on the information structure, we separate each agent’s estimation and control problems. The BS aims to find the optimum scheduling policy that minimizes a weighted age of information based performance metric, subject to the hard-bandwidth constraint. We first relax the hard constraint to a soft update-rate constraint and compute an optimal policy for the relaxed problem by reformulating it into an MDP. This then inspires a sub-optimal policy for the bandwidth constrained problem, which is shown to approach the optimal policy as \u0000<inline-formula> <tex-math>$N rightarrow infty $ </tex-math></inline-formula>\u0000. Next, we solve the consensus problem using the mean-field game framework. By explicitly constructing the mean-field system, we prove the existence of a unique mean-field equilibrium. Consequently, we show that the equilibrium policies obtained constitute an \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000–Nash equilibrium for the finite-agent system.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"682-697"},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138678678","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 : 2023-11-09DOI: 10.1109/JSAIT.2023.3329121
Giuseppe Cocco;Andrea Munari;Gianluigi Liva
We study a system in which two-state Markov sources send status updates to a common receiver over a slotted ALOHA random access channel. We characterize the performance of the system in terms of state estimation entropy (SEE), which measures the uncertainty at the receiver about the sources’ state. Two channel access strategies are considered: a reactive policy that depends on the source behaviour and a random one that is independent of it. We prove that the considered policies can be studied using two different hidden Markov models and show through a density evolution analysis that the reactive strategy outperforms the random one in terms of SEE while the opposite is true for age of information. Furthermore, we characterize the probability of error in the state estimation at the receiver, considering a maximum a posteriori and a low-complexity (decode & hold) estimator. Our study provides useful insights on the design trade-offs that emerge when different performance metrics are adopted. Moreover, we show how the source statistics significantly impact the system performance.
我们研究了一个系统，在这个系统中，双状态马尔可夫信号源通过插槽式 ALOHA 随机接入信道向一个共同接收器发送状态更新。我们用状态估计熵（SEE）来描述系统的性能，该熵衡量接收方对信源状态的不确定性。我们考虑了两种信道接入策略：一种是取决于信源行为的反应策略，另一种是与信源行为无关的随机策略。我们证明可以使用两种不同的隐马尔可夫模型来研究所考虑的策略，并通过密度演化分析表明，就 SEE 而言，反应策略优于随机策略，而信息年龄则相反。此外，考虑到最大后验和低复杂度（解码与保持）估计器，我们还描述了接收器状态估计的错误概率。我们的研究为采用不同性能指标时出现的设计权衡提供了有用的见解。此外，我们还展示了信号源统计如何对系统性能产生重大影响。
{"title":"Remote Monitoring of Two-State Markov Sources via Random Access Channels: An Information Freshness vs. State Estimation Entropy Perspective","authors":"Giuseppe Cocco;Andrea Munari;Gianluigi Liva","doi":"10.1109/JSAIT.2023.3329121","DOIUrl":"10.1109/JSAIT.2023.3329121","url":null,"abstract":"We study a system in which two-state Markov sources send status updates to a common receiver over a slotted ALOHA random access channel. We characterize the performance of the system in terms of state estimation entropy (SEE), which measures the uncertainty at the receiver about the sources’ state. Two channel access strategies are considered: a reactive policy that depends on the source behaviour and a random one that is independent of it. We prove that the considered policies can be studied using two different hidden Markov models and show through a density evolution analysis that the reactive strategy outperforms the random one in terms of SEE while the opposite is true for age of information. Furthermore, we characterize the probability of error in the state estimation at the receiver, considering a maximum a posteriori and a low-complexity (decode & hold) estimator. Our study provides useful insights on the design trade-offs that emerge when different performance metrics are adopted. Moreover, we show how the source statistics significantly impact the system performance.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"651-666"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135560847","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}
Intelligent real-time applications, such as video surveillance, demand intensive computation to extract status information from raw sensing data. This poses a substantial challenge in orchestrating computation and communication resources to provide fresh status information. In this paper, we consider a scenario where multiple energy-constrained devices served by an edge server. To extract status information, each device can either do the computation locally or offload it to the edge server. A scheduling policy is needed to determine when and where to compute for each device, taking into account communication and computation capabilities, as well as task-specific timeliness requirements. To that end, we first model the timeliness requirements as general penalty functions of Age of Information (AoI). A convex optimization problem is formulated to provide a lower bound of the minimum AoI penalty given system parameters. Using KKT conditions, we proposed a novel scheduling policy which evaluates status update priorities based on communication and computation delays and task-specific timeliness requirements. The proposed policy is applied to an object tracking application and carried out on a large video dataset. Simulation results show that our policy improves tracking accuracy compared with scheduling policies based on video content information.
{"title":"Optimizing Task-Specific Timeliness With Edge-Assisted Scheduling for Status Update","authors":"Jingzhou Sun;Lehan Wang;Zhaojun Nan;Yuxuan Sun;Sheng Zhou;Zhisheng Niu","doi":"10.1109/JSAIT.2023.3329017","DOIUrl":"10.1109/JSAIT.2023.3329017","url":null,"abstract":"Intelligent real-time applications, such as video surveillance, demand intensive computation to extract status information from raw sensing data. This poses a substantial challenge in orchestrating computation and communication resources to provide fresh status information. In this paper, we consider a scenario where multiple energy-constrained devices served by an edge server. To extract status information, each device can either do the computation locally or offload it to the edge server. A scheduling policy is needed to determine when and where to compute for each device, taking into account communication and computation capabilities, as well as task-specific timeliness requirements. To that end, we first model the timeliness requirements as general penalty functions of Age of Information (AoI). A convex optimization problem is formulated to provide a lower bound of the minimum AoI penalty given system parameters. Using KKT conditions, we proposed a novel scheduling policy which evaluates status update priorities based on communication and computation delays and task-specific timeliness requirements. The proposed policy is applied to an object tracking application and carried out on a large video dataset. Simulation results show that our policy improves tracking accuracy compared with scheduling policies based on video content information.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"624-638"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134981772","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 : 2023-11-02DOI: 10.1109/JSAIT.2023.3328651
Kang Du;Yu Xiang
It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution shifts. One principled approach is to adopt the structural causal models to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle might be violated in practical settings when the response is intervened. A natural question is whether it is still possible to identify other forms of invariance to facilitate prediction in unseen environments. To shed light on this challenging scenario, we focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP), an explicit relation to capture interventions through an additional feature, leading to an alternative form of invariance that enables a unified treatment of general interventions on the response as well as the predictors. We analyze the asymptotic generalization errors of our method under both the discrete and continuous environment settings, where the continuous case is handled by relating it to the semiparametric varying coefficient models. We present algorithms that show competitive performance compared to existing methods over various experimental settings including a COVID dataset.
{"title":"Learning Invariant Representations Under General Interventions on the Response","authors":"Kang Du;Yu Xiang","doi":"10.1109/JSAIT.2023.3328651","DOIUrl":"10.1109/JSAIT.2023.3328651","url":null,"abstract":"It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution shifts. One principled approach is to adopt the structural causal models to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle might be violated in practical settings when the response is intervened. A natural question is whether it is still possible to identify other forms of invariance to facilitate prediction in unseen environments. To shed light on this challenging scenario, we focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP), an explicit relation to capture interventions through an additional feature, leading to an alternative form of invariance that enables a unified treatment of general interventions on the response as well as the predictors. We analyze the asymptotic generalization errors of our method under both the discrete and continuous environment settings, where the continuous case is handled by relating it to the semiparametric varying coefficient models. We present algorithms that show competitive performance compared to existing methods over various experimental settings including a COVID dataset.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"808-819"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134887604","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 : 2023-11-01DOI: 10.1109/JSAIT.2023.3329431
Karim Banawan;Ahmed Arafa;Karim G. Seddik
We consider a multi-process remote estimation system observing $K$ independent Ornstein-Uhlenbeck processes. In this system, a shared sensor samples the $K$ processes in such a way that the long-term average sum mean square error (MSE) is minimized using signal-independent sampling policies, in which sampling instances are chosen independently from the processes’ values. The sensor operates under a total sampling frequency constraint $f_{max }$ . The samples from all processes consume random processing delays in a shared queue and then are transmitted over an erasure channel with probability $epsilon $ . We study two variants of the problem: first, when the samples are scheduled according to a Maximum-Age-First (MAF) policy, and the receiver provides an erasure status feedback; and second, when samples are scheduled according to a Round-Robin (RR) policy, when there is no erasure status feedback from the receiver. Aided by optimal structural results, we show that the optimal sampling policy for both settings, under some conditions, is a threshold policy. We characterize the optimal threshold and the corresponding optimal long-term average sum MSE as a function of $K$ , $f_{max }$ , $epsilon $ , and the statistical properties of the observed processes. Our results show that, with an exponentially distributed service rate, the optimal threshold $tau ^{ast}$ increases as the number of processes $K$ increases, for both settings. Additionally, we show that the optimal threshold is an increasing function of $epsilon $ in the case of available erasure status feedback, while it exhibits the opposite behavior, i.e., $tau ^{ast}$ is a decreasing function of $epsilon $ , in the case of absent erasure status feedback.
我们考虑了一个观察K个独立的Ornstein-Uhlenbeck过程的多过程远程估计系统。在该系统中，共享传感器以这样一种方式对K个过程进行采样，即使用与信号无关的采样策略最小化长期平均和均方误差(MSE)，其中采样实例的选择独立于过程的值。传感器在总采样频率约束下工作。来自所有进程的采样在共享队列中消耗随机处理延迟，然后以概率通过擦除通道传输。我们研究了该问题的两种变体:第一，当样本按照最大年龄优先(maximum - age first, MAF)策略进行调度时，接收方提供擦除状态反馈;第二种情况是，当采样按RR (Round-Robin)策略调度时，当接收方没有擦除状态反馈时。在最优结构结果的帮助下，我们证明了在某些条件下，两种设置的最优抽样策略是阈值策略。我们将最佳阈值和相应的最佳长期平均和MSE描述为K, f和观察过程的统计特性的函数。结果表明，在服务率呈指数分布的情况下，对于两种设置，最优阈值τ*都随着进程数K的增加而增加。此外，我们证明了在可用的擦除状态反馈情况下，最优阈值是一个增加函数，而在没有擦除状态反馈的情况下，它表现出相反的行为，即τ*是一个减小函数。
{"title":"Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback: Signal-Independent Policies","authors":"Karim Banawan;Ahmed Arafa;Karim G. Seddik","doi":"10.1109/JSAIT.2023.3329431","DOIUrl":"10.1109/JSAIT.2023.3329431","url":null,"abstract":"We consider a multi-process remote estimation system observing \u0000<inline-formula> <tex-math>$K$ </tex-math></inline-formula>\u0000 independent Ornstein-Uhlenbeck processes. In this system, a shared sensor samples the \u0000<inline-formula> <tex-math>$K$ </tex-math></inline-formula>\u0000 processes in such a way that the long-term average sum mean square error (MSE) is minimized using signal-independent sampling policies, in which sampling instances are chosen independently from the processes’ values. The sensor operates under a total sampling frequency constraint \u0000<inline-formula> <tex-math>$f_{max }$ </tex-math></inline-formula>\u0000. The samples from all processes consume random processing delays in a shared queue and then are transmitted over an erasure channel with probability \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000. We study two variants of the problem: first, when the samples are scheduled according to a Maximum-Age-First (MAF) policy, and the receiver provides an erasure status feedback; and second, when samples are scheduled according to a Round-Robin (RR) policy, when there is no erasure status feedback from the receiver. Aided by optimal structural results, we show that the optimal sampling policy for both settings, under some conditions, is a threshold policy. We characterize the optimal threshold and the corresponding optimal long-term average sum MSE as a function of \u0000<inline-formula> <tex-math>$K$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$f_{max }$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000, and the statistical properties of the observed processes. Our results show that, with an exponentially distributed service rate, the optimal threshold \u0000<inline-formula> <tex-math>$tau ^{ast}$ </tex-math></inline-formula>\u0000 increases as the number of processes \u0000<inline-formula> <tex-math>$K$ </tex-math></inline-formula>\u0000 increases, for both settings. Additionally, we show that the optimal threshold is an increasing function of \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000 in the case of available erasure status feedback, while it exhibits the opposite behavior, i.e., \u0000<inline-formula> <tex-math>$tau ^{ast}$ </tex-math></inline-formula>\u0000 is a decreasing function of \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000, in the case of absent erasure status feedback.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"607-623"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135362790","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 : 2023-11-01DOI: 10.1109/JSAIT.2023.3328476
Jun Wu;Mathias Drton
Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data is available, each DAG can be identified only up to a Markov equivalence class. In contrast, recent work has shown that the DAG can be uniquely identified if the errors in the model are homoscedastic, i.e., all have the same variance. This equal variance assumption yields methods that, if appropriate, are highly scalable and also sheds light on fundamental information-theoretic limits and optimality in causal discovery. In this paper, we fill the gap that exists between the two previously considered cases, which assume the error variances to be either arbitrary or all equal. Specifically, we formulate a framework of partial homoscedasticity, in which the variables are partitioned into blocks and each block shares the same error variance. For any such groupwise equal variances assumption, we characterize when two DAGs give rise to identical Gaussian linear structural equation models. Furthermore, we show how the resulting distributional equivalence classes may be represented using a completed partially directed acyclic graph (CPDAG), and we give an algorithm to efficiently construct this CPDAG. In a simulation study, we demonstrate that greedy search provides an effective way to learn the CPDAG and exploit partial knowledge about homoscedasticity of errors in structural equation models.
递归线性结构方程模型和相关的有向无环图（DAG）在因果发现中发挥着重要作用。这类模型的经典可识别性结果表明，当只有观测数据时，每个 DAG 只能识别到马尔可夫等价类。相反，最近的研究表明，如果模型中的误差是同方差的，即所有误差都具有相同的方差，那么 DAG 就可以唯一地识别出来。这种等方差假设产生的方法，如果合适，具有很强的可扩展性，同时也揭示了因果发现中基本的信息论极限和最优性。在本文中，我们填补了之前考虑的两种情况之间的空白，即假设误差方差要么任意，要么全部相等。具体来说，我们提出了一个部分同方差的框架，在这个框架中，变量被划分成块，每个块共享相同的误差方差。对于任何这样的分组等方差假设，我们都会描述两个 DAG 何时会产生相同的高斯线性结构方程模型。此外，我们还展示了如何用一个完整的部分有向无环图（CPDAG）来表示所产生的分布等价类，并给出了一种高效构建 CPDAG 的算法。在模拟研究中，我们证明了贪婪搜索是学习 CPDAG 和利用结构方程模型中误差同方差性部分知识的有效方法。
{"title":"Partial Homoscedasticity in Causal Discovery With Linear Models","authors":"Jun Wu;Mathias Drton","doi":"10.1109/JSAIT.2023.3328476","DOIUrl":"10.1109/JSAIT.2023.3328476","url":null,"abstract":"Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data is available, each DAG can be identified only up to a Markov equivalence class. In contrast, recent work has shown that the DAG can be uniquely identified if the errors in the model are homoscedastic, i.e., all have the same variance. This equal variance assumption yields methods that, if appropriate, are highly scalable and also sheds light on fundamental information-theoretic limits and optimality in causal discovery. In this paper, we fill the gap that exists between the two previously considered cases, which assume the error variances to be either arbitrary or all equal. Specifically, we formulate a framework of partial homoscedasticity, in which the variables are partitioned into blocks and each block shares the same error variance. For any such groupwise equal variances assumption, we characterize when two DAGs give rise to identical Gaussian linear structural equation models. Furthermore, we show how the resulting distributional equivalence classes may be represented using a completed partially directed acyclic graph (CPDAG), and we give an algorithm to efficiently construct this CPDAG. In a simulation study, we demonstrate that greedy search provides an effective way to learn the CPDAG and exploit partial knowledge about homoscedasticity of errors in structural equation models.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"639-650"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10304270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135360763","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 : 2023-11-01DOI: 10.1109/JSAIT.2023.3329034
Kumar Saurav;Rahul Vaze
We consider a node where packets of fixed size (inbits) are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on the packet availability and the current AoI, the node can choose which packet to transmit, and at what transmission speed (in bits per second). Power consumption is a monotonically increasing convex function of the transmission speed. In this paper, for any given time horizon, the objective is to find a causal policy that minimizes the total energy consumption while satisfying the peak AoI constraint. We consider competitive ratio as the performance metric, that is defined as the ratio of the expected cost of a causal policy, and the expected cost of an optimal offline policy that knows the input (packet generation times) in advance. We first derive a lower bound on the competitive ratio of all causal policies, in terms of the system parameters (such as power function, packet size and peak AoI threshold), and then propose a particular policy for which we show that its competitive ratio has similar order of dependence on the system parameters as the derived lower bound.
{"title":"Online Energy Minimization Under a Peak Age of Information Constraint","authors":"Kumar Saurav;Rahul Vaze","doi":"10.1109/JSAIT.2023.3329034","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3329034","url":null,"abstract":"We consider a node where packets of fixed size (inbits) are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on the packet availability and the current AoI, the node can choose which packet to transmit, and at what transmission speed (in bits per second). Power consumption is a monotonically increasing convex function of the transmission speed. In this paper, for any given time horizon, the objective is to find a causal policy that minimizes the total energy consumption while satisfying the peak AoI constraint. We consider competitive ratio as the performance metric, that is defined as the ratio of the expected cost of a causal policy, and the expected cost of an optimal offline policy that knows the input (packet generation times) in advance. We first derive a lower bound on the competitive ratio of all causal policies, in terms of the system parameters (such as power function, packet size and peak AoI threshold), and then propose a particular policy for which we show that its competitive ratio has similar order of dependence on the system parameters as the derived lower bound.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"579-590"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431090","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 : 2023-10-31DOI: 10.1109/JSAIT.2023.3328766
Markus Fidler;Jaya Prakash Champati;Joerg Widmer;Mahsa Noroozi
This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of $text{M}mid text{M}mid 1$ queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of $text{G}mid text{G}mid 1$ queues. Tail bounds of the age-of-information of independent parallel queues follow readily. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.
{"title":"Statistical Age-of-Information Bounds for Parallel Systems: When Do Independent Channels Make a Difference?","authors":"Markus Fidler;Jaya Prakash Champati;Joerg Widmer;Mahsa Noroozi","doi":"10.1109/JSAIT.2023.3328766","DOIUrl":"10.1109/JSAIT.2023.3328766","url":null,"abstract":"This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of \u0000<inline-formula> <tex-math>$text{M}mid text{M}mid 1$ </tex-math></inline-formula>\u0000 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of \u0000<inline-formula> <tex-math>$text{G}mid text{G}mid 1$ </tex-math></inline-formula>\u0000 queues. Tail bounds of the age-of-information of independent parallel queues follow readily. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"591-606"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10302220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262828","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}
We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.
{"title":"Learning Linear Gaussian Polytree Models With Interventions","authors":"Daniele Tramontano;L. Waldmann;M. Drton;Eliana Duarte","doi":"10.1109/JSAIT.2023.3328429","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3328429","url":null,"abstract":"We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"569-578"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795150","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 : 2023-10-12DOI: 10.1109/JSAIT.2023.3322077
Kumar Saurav;Rahul Vaze
Finding an optimal/near-optimal scheduling algorithm to minimize the age of information (AoI) in a multi-source G/G/1 system is well-known to be a hard problem, more so if there is a transmission (energy) cost. In this paper, we consider a multi-source G/G/1 system and the goal is to minimize a weighted sum of the AoI of all sources, subject to an energy cost constraint. We propose a novel doubly randomized non-preemptive scheduling algorithm and show that in the non-preemptive setting, where an update under transmission cannot be preempted, the competitive ratio of the proposed algorithm is at most 3 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources. Notably, the competitive ratio is independent of the number of sources, or their service time distributions, and is at most 4 for several common update inter-generation time distributions such as exponential, uniform and Rayleigh. For preemptive setting, where an update under transmission can be preempted, we consider a multi-source G/M/1 system and show that the proposed non-preemptive algorithm has competitive ratio at most 5 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources.
{"title":"Scheduling to Minimize Age of Information With Multiple Sources","authors":"Kumar Saurav;Rahul Vaze","doi":"10.1109/JSAIT.2023.3322077","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3322077","url":null,"abstract":"Finding an optimal/near-optimal scheduling algorithm to minimize the age of information (AoI) in a multi-source G/G/1 system is well-known to be a hard problem, more so if there is a transmission (energy) cost. In this paper, we consider a multi-source G/G/1 system and the goal is to minimize a weighted sum of the AoI of all sources, subject to an energy cost constraint. We propose a novel doubly randomized non-preemptive scheduling algorithm and show that in the non-preemptive setting, where an update under transmission cannot be preempted, the competitive ratio of the proposed algorithm is at most 3 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources. Notably, the competitive ratio is independent of the number of sources, or their service time distributions, and is at most 4 for several common update inter-generation time distributions such as exponential, uniform and Rayleigh. For preemptive setting, where an update under transmission can be preempted, we consider a multi-source G/M/1 system and show that the proposed non-preemptive algorithm has competitive ratio at most 5 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"539-550"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109157409","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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