In this correspondence, we correct the following points in the above paper.

This paper studies the convergence of clipped stochastic gradient descent (SGD) algorithms with decision-dependent data distribution. Our setting is motivated by privacy preserving optimization algorithms that interact with performative data where the prediction models can influence future outcomes. This challenging setting involves the non-smooth clipping operator and non-gradient dynamics due to distribution shifts. We make two contributions in pursuit for a performative stable solution with these algorithms. First, we characterize the stochastic bias with projected clipped SGD (PCSGD) algorithm which is caused by the clipping operator that prevents PCSGD from reaching a stable solution. When the loss function is strongly convex, we quantify the lower and upper bounds for this stochastic bias and demonstrate a bias amplification phenomenon with the sensitivity of data distribution. When the loss function is non-convex, we bound the magnitude of stationarity bias. Second, we propose remedies to mitigate the bias either by utilizing an optimal step size design for PCSGD, or to apply the recent DiceSGD algorithm [Zhang et al., 2024]. Our analysis is also extended to show that the latter algorithm is free from stochastic bias in the performative setting. Numerical experiments verify our findings.

Cyber–physical multiagent systems are driving rapid technological advancements that automate a wide range of critical functions, thereby enabling safer, more accessible, and more efficient autonomous operations across diverse sectors. We refer to the capability of such systems to self-organize and coordinate toward accomplishing shared objectives as autonomy. The unique characteristics of these systems prompt a reevaluation of their security concepts, including their vulnerabilities, and mechanisms to mitigate these vulnerabilities. This survey article examines how advancements in wireless networking, coupled with sensing and computing capabilities, can foster novel security concepts for autonomous cyber–physical systems (CPSs). It delves into three main themes related to securing multiagent CPSs. First, we discuss the threats that are particularly relevant to multiagent CPSs, given the potential lack of trustworthiness between agents. Second, we present prospects for sensing, contextual awareness, and authentication, enabling the inference and measurement of a form of interagent “quantitative trust” or “cy-trust” for these systems. Third, we elaborate on the application of quantifiable trust notions to enable “resilient coordination,” where “resilient” signifies sustained functionality amid attacks on multiagent CPSs. This survey unveils the cyber–physical character of future interconnected systems as a pivotal catalyst for realizing robust autonomy.

In this article, we develop a resilient binary hypothesis testing framework for decision making in adversarial multirobot crowdsensing tasks. This framework exploits stochastic trust observations between robots to arrive at tractable, resilient decision making at a centralized fusion center (FC) even when, first, there exist malicious robots in the network and their number may be larger than the number of legitimate robots, and second, the FC uses one-shot noisy measurements from all robots. We derive two algorithms to achieve this. The first is the two-stage approach (2SA) that estimates the legitimacy of robots based on received trust observations, and provably minimizes the probability of detection error in the worst-case malicious attack. For the 2SA, we assume that the proportion of malicious robots is known but arbitrary. For the case of an unknown proportion of malicious robots, we develop the adversarial generalized likelihood ratio test (A-GLRT) that uses both the reported robot measurements and trust observations to simultaneously estimate the trustworthiness of robots, their reporting strategy, and the correct hypothesis. We exploit particular structures in the problem to show that this approach remains computationally tractable even with unknown problem parameters. We deploy both algorithms in a hardware experiment where a group of robots conducts crowdsensing of traffic conditions subject to a Sybil attack on a mock-up road network. We extract the trust observations for each robot from communication signals, which provide statistical information on the uniqueness of the sender. We show that even when the malicious robots are in the majority, the FC can reduce the probability of detection error to 30.5% and 29% for the 2SA and the A-GLRT algorithms, respectively.

Intermittent connectivity of clients to the parameter server (PS) is a major bottleneck in federated edge learning frameworks. The lack of constant connectivity induces a large generalization gap, especially when the local data distribution amongst clients exhibits heterogeneity. To overcome intermittent communication outages between clients and the central PS, we introduce the concept of collaborative relaying wherein the participating clients relay their neighbors’ local updates to the PS in order to boost the participation of clients with poor connectivity to the PS. We propose a semi-decentralized federated learning framework in which at every communication round, each client initially computes a local averaging of a subset of its neighboring clients’ updates, and eventually transmits to the PS a weighted average of its own update and those of its neighbors’. We appropriately optimize these local averaging weights to ensure that the global update at the PS is unbiased with minimal variance – consequently improving the convergence rate. Numerical evaluations on the CIFAR-10 dataset demonstrate that our collaborative relaying approach outperforms federated averaging-based benchmarks for learning over intermittently-connected networks such as when the clients communicate over millimeter wave channels with intermittent blockages.

We develop a resilient binary hypothesis testing frame-work for decision making in adversarial multi-robot crowdsensing tasks. This framework exploits stochastic trust observations between robots to arrive at tractable, resilient decision making at a centralized Fusion Center (FC) even when i) there exist malicious robots in the network and their number may be larger than the number of legitimate robots, and ii) the FC uses one-shot noisy measurements from all robots. We derive two algorithms to achieve this. The first is the Two Stage Approach (2SA) that estimates the legitimacy of robots based on received trust observations, and provably minimizes the probability of detection error in the worst-case malicious attack. Here, the proportion of malicious robots is known but arbitrary. For the case of an unknown proportion of malicious robots, we develop the Adversarial Generalized Likelihood Ratio Test (A-GLRT) that uses both the reported robot measurements and trust observations to estimate the trustworthiness of robots, their reporting strategy, and the correct hypothesis simultaneously. We exploit special problem structure to show that this approach remains computationally tractable despite several unknown problem parameters. We deploy both algorithms in a hardware experiment where a group of robots conducts crowdsensing of traffic conditions on a mock-up road network similar in spirit to Google Maps, subject to a Sybil attack. We extract the trust observations for each robot from actual communication signals which provide statistical information on the uniqueness of the sender. We show that even when the malicious robots are in the majority, the FC can reduce the probability of detection error to 30.5% and 29% for the 2SA and the A-GLRT respectively.

This work considers the problem of Distributed Mean Estimation (DME) over networks with intermittent connectivity, where the goal is to learn a global statistic over the data samples localized across distributed nodes with the help of a central server. To mitigate the impact of intermittent links, nodes can collaborate with their neighbors to compute local consensus which they forward to the central server. In such a setup, the communications between any pair of nodes must satisfy local differential privacy constraints. We study the tradeoff between collaborative relaying and privacy leakage due to the additional data sharing among nodes and, subsequently, propose a novel differentially private collaborative algorithm for DME to achieve the optimal tradeoff. Finally, we present numerical simulations to substantiate our theoretical findings.

This paper introduces the informational multi-armed bandit (IMAB) model, in which at each round, a player chooses an arm, observes a symbol, and receives an unobserved reward in the form of the symbol’s self-information. Thus, the expected reward of an arm is the Shannon entropy of the probability mass function of the source that generates its symbols. The player aims to maximize the expected total reward associated with the entropy values of the arms played. Under the assumption that the alphabet size is known, two UCB-based algorithms are proposed for the IMAB model which consider the biases of the plug-in entropy estimator. The first algorithm optimistically corrects the bias term in the entropy estimation. The second algorithm relies on data-dependent confidence intervals that adapt to sources with small entropy values. Performance guarantees are provided by upper bounding the expected regret of each of the algorithms. Furthermore, in the Bernoulli case, the asymptotic behavior of these algorithms is compared to the Lai-Robbins lower bound for the pseudo regret. Additionally, under the assumption that the exact alphabet size is unknown, and instead the player only knows a loose upper bound on it, a UCB-based algorithm is proposed, in which the player aims to reduce the regret caused by the unknown alphabet size in a finite time regime. Numerical results illustrating the expected regret of the algorithms presented in the paper are provided.

We consider a centralized detection problem where sensors experience noisy measurements and intermittent connectivity to a centralized fusion center. The sensors collaborate locally within predefined sensor clusters and fuse their noisy sensor data to reach a common local estimate of the detected event in each cluster. The connectivity of each sensor cluster is intermittent and depends on the available communication opportunities of the sensors to the fusion center. Upon receiving the estimates from all the connected sensor clusters the fusion center fuses the received estimates to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a cloud-cluster architecture. We propose a method for optimizing the decision rule for each cluster and analyzing the expected detection performance resulting from our hybrid scheme. Our method is tractable and addresses the high computational complexity caused by heterogeneous sensors’ and clusters’ detection quality, heterogeneity in their communication opportunities, and non-convexity of the loss function. Our analysis shows that clustering the sensors provides resilience to noise in the case of low sensor communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.

We consider an extension to the restless multi-armed bandit (RMAB) problem with unknown arm dynamics, where an unknown exogenous global Markov process governs the rewards distribution of each arm. Under each global state, the rewards process of each arm evolves according to an unknown Markovian rule, which is non-identical among different arms. At each time, a player chooses an arm out of N arms to play, and receives a random reward from a finite set of reward states. The arms are restless, that is, their local state evolves regardless of the player’s actions. The objective is an arm-selection policy that minimizes the regret, defined as the reward loss with respect to a player that knows the dynamics of the problem, and plays at each time t the arm that maximizes the expected immediate value. We develop the Learning under Exogenous Markov Process (LEMP) algorithm, that achieves a logarithmic regret order with time, and a finite-sample bound on the regret is established. Simulation results support the theoretical study and demonstrate strong performances of LEMP.

We introduce a multi-armed bandit problem with information-based rewards. At each round, a player chooses an arm, observes a symbol, and receives an unobserved reward in the form of the symbol’s self-information. The player aims to maximize the expected total reward associated with the entropy values of the arms played. We propose two algorithms based on upper confidence bounds (UCB) for this model. The first algorithm optimistically corrects the bias term in the entropy estimation. The second algorithm relies on data-dependent UCBs that adapt to sources with small entropy values. We provide performance guarantees by upper bounding the expected regret of each of the algorithms, and compare their asymptotic behavior to the Lai-Robbins lower bound. Finally, we provide numerical results illustrating the regret of the algorithms presented.

We present a semi-decentralized federated learning algorithm wherein clients collaborate by relaying their neighbors’ local updates to a central parameter server (PS). At every communication round to the PS, each client computes a local consensus of the updates from its neighboring clients and eventually transmits a weighted average of its own update and those of its neighbors to the PS. We appropriately optimize these averaging weights to ensure that the global update at the PS is unbiased and to reduce the variance of the global update at the PS, consequently improving the rate of convergence. Numerical simulations substantiate our theoretical claims and demonstrate settings with intermittent connectivity between the clients and the PS, where our proposed algorithm shows an improved convergence rate and accuracy in comparison with the federated averaging algorithm.

This work considers the problem of resilient consensus, where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: First, almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network connectivity; second, the deviation of the converged limit, from the case where there is no attack, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially; and third correct classification of malicious and legitimate agents can be attained in finite time almost surely. Furthermore, the expected convergence rate decays exponentially as a function of the quality of the trust observations between agents.

We consider a detection problem where sensors experience noisy measurements and intermittent communication opportunities to a centralized fusion center (or cloud). The objective of the problem is to arrive at the correct estimate of event detection in the environment. The sensors may communicate locally with other sensors (local clusters) where they fuse their noisy sensor data to estimate the detection of an event locally. In addition, each sensor cluster can intermittently communicate to the cloud, where a centralized fusion center fuses estimates from all sensor clusters to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a cloud-cluster architecture. Minimizing the expected loss function of networks where noisy sensors are intermittently connected to the cloud, as in our hybrid communication scheme, has not been investigated to our knowledge. We leverage recently improved concentration inequalities to arrive at an optimized decision rule for each cluster and we analyze the expected detection performance resulting from our hybrid scheme. Our analysis shows that clustering the sensors provides resilience to noise in the case of low communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.

This work presents a new optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework, resources are allocated within virtual cells encompassing several base-stations and the users within their coverage areas. We form the virtual cells using hierarchical clustering with a minimax linkage criterion given a particular number of such cells. Once the virtual cells are formed, we consider a single-user detection interference coordination model in which base-stations in a virtual cell jointly allocate the channels and power to users within the virtual cell. We propose two new schemes for solving this mixed integer NP- hard resource allocation problem. The first scheme transforms the problem into a continuous variables problem; the second scheme proposes a new channel allocation method and then alternately solves the channel allocation problem using this new method, and the power allocation problem. We evaluate the average system sum rate of these schemes for a variable number of virtual cells. These results quantify the sum-rate along a continuum of fully- centralized versus fully-distributed optimization for different clustering and resource allocation strategies. These results indicate that the penalty of fully-distributed optimization versus fully-centralized (cloud RAN) can be as high as 50%. However, if designed properly, a few base stations within a virtual cell using neighborhood- based optimization have almost the same performance as fully-centralized optimization.

This work presents a new resource allocation optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework resources are allocated within virtual cells encompassing several base-stations and the users within their coverage area. Incorporating the virtual cell concept enables the utilization of more sophisticated cooperative communication schemes such as coordinated multi-point decoding. We form the virtual cells using hierarchical clustering given a particular number of such cells. Once the virtual cells are formed, we consider a cooperative decoding scheme in which the base-stations in each virtual cell jointly decode the signals that they receive. We propose an iterative solution for the resource allocation problem resulting from the cooperative decoding within each virtual cell. Numerical results for the average system sum rate of our network design under hierarchical clustering are presented. These results indicate that virtual cells with neighborhood-based optimization leads to significant gains in sum rate over optimization within each cell, yet may also have a significant sum-rate penalty compared to fully-centralized optimization.

In this paper, we consider the simultaneous connectivity of primary and secondary networks forming a cognitive model. It is assumed that the cognitive model includes guard zones that prevent the nodes of the secondary network from being active in the vicinity of primary nodes to limit interference. Under these assumptions, we characterize the region of densities, the transmission radii of the nodes in each of the networks, and the guard zones for which the two networks have a unique unbounded connected component. We prove that this model is feasible, that is, there exists simultaneous connectivity with the unique unbounded connected component in each of the networks. We also provide necessary and sufficient conditions for the simultaneous connectivity of this cognitive model.

In this paper, we investigate the global energy efficiency of a bidirectional amplify-and-forward relay MIMO system. It is assumed that the relay serves two end-users, each requiring a minimum target rate. Two algorithms are proposed, a suboptimal one with lower complexity, and an optimal one with slightly higher complexity. We present numerical results that compare the two algorithms and exhibit several optimality properties concerning the global energy efficiency function.

In this paper we analyze the connectivity of cognitive radio ad-hoc networks. Contrary to previous works, we pursue the connectivity of both the primary and secondary networks, a state we call “simultaneous connectivity”. We determine that if the networks are simultaneously connected then their infinite connected components are unique. In addition, we characterize the region of densities in which both the primary and secondary networks have a unique infinite connected component.

In this paper, we introduce the two-user asynchronous cognitive multiple access channel (ACMAC). This channel model includes two transmitters, an uninformed one and an informed one, which knows prior to the beginning of a transmission the message which the uninformed transmitter is about to send. We assume that the channel from the uninformed transmitter to the receiver suffers a fixed but unknown delay. We further introduce a modified model, referred to as the asynchronous codeword cognitive multiple access channel (ACC-MAC), which differs from the ACMAC in that the informed user knows the signal that is to be transmitted by the other user, rather than the message that it is about to transmit. We state inner and outer bounds on the ACMAC and the ACC-MAC capacity regions, and we specialize the results to the Gaussian case. Furthermore, we characterize the capacity regions of these channels in terms of multi-letter expressions. Finally, we provide an example that instantiates the difference between message side-information and codeword side-information.

Several channels with asynchronous side information are introduced. We first consider single-user state-dependent channels with asynchronous side information at the transmitter. It is assumed that the state information sequence is a possibly delayed version of the state sequence, and that the encoder and the decoder are aware of the fact that the state information might be delayed. It is additionally assumed that an upper bound on the delay is known to both the encoder and the decoder, but other than that, they are ignorant of the actual delay. We consider both the causal and the noncausal cases and present achievable rates for these channels, and the corresponding coding schemes. We find the capacity of the asynchronous Gel'fand-Pinsker channel with feedback. Finally, we consider a memoryless state-dependent channel with asynchronous side information at both the transmitter and the receiver, and establish a single-letter expression for its capacity.

We introduce the asynchronous cognitive multiple-access channel with an uninformed encoder and an informed one. We assume that the informed encoder knows in advance the message of the uninformed encoder and consequently its codeword, up to some delay. In addition, the informed encoder knows the set of all possible delays in the channel. We characterize the capacity region of the ACMAC in terms of multi-letter expressions. In addition, we present single-letter inner and outer bounds on the capacity region of this channel. We conclude by studying the special case of the Gaussian asynchronous multiple-access channels with an uninformed encoder.