We study a communication scheduling and remote estimation problem within a worst-case scenario that involves a strategic adversary. Specially, a remote sensing system consisting of a sensor, an ...encoder and a decoder is configured to observe, transmit, and recover a discrete time stochastic process. At each time step, the sensor makes an observation on the state variable of the stochastic process. The sensor is constrained by the number of transmissions over the time horizon, and thus it needs to decide whether to transmit its observation or not after making each measurement. If the sensor decides to transmit, it sends the observation to the encoder, who then encodes and transmits the observation to the decoder. Otherwise, the sensor and the encoder maintain silence. The decoder is required to generate a real-time estimate on the state variable. The sensor, the encoder, and the decoder collaborate to minimize the sum of the communication cost for the sensor, the encoding cost for the encoder, and the estimation error for the decoder. There is also a jammer interfering with the communication between the encoder and the decoder, by injecting an additive channel noise to the communication channel. The jammer is charged for the jamming power and is rewarded for the estimation error generated by the decoder, and it aims to minimize its net cost. We consider a feedback Stackelberg game with the sensor, the encoder, and the decoder as the composite leader, and the jammer as the follower. Under some technical assumptions, we obtain a feedback Stackelberg solution, which is threshold based for the scheduler, and piecewise affine for the encoder and the decoder. We also generate numerical results to demonstrate the performance of the remote sensing system under the feedback Stackelberg solution.
This paper analyzes the information disclosure problems originated in economics through the lens of information theory. Such problems are radically different from the conventional communication ...paradigms in information theory since they involve different objectives for the encoder and the decoder, which are aware of this mismatch and act accordingly. This leads, in our setting, to a hierarchical communication game, where the transmitter announces an encoding strategy with full commitment, and its distortion measure depends on a private information sequence whose realization is available at the transmitter. The receiver decides on its decoding strategy that minimizes its own distortion based on the announced encoding map and the statistics. Three problem settings are considered, focusing on the quadratic distortion measures, and jointly Gaussian source and private information: compression, communication, and the simple equilibrium conditions without any compression or communication. The equilibrium strategies and associated costs are characterized. The analysis is then extended to the receiver side information setting and the major changes in structure of optimal strategies are identified. Finally, an extension of the results to the broader context of decentralized stochastic control is presented.
This article studies novel attack and defense strategies, based on a class of stealthy attacks, namely the zero-dynamics attack (ZDA), for multiagent control systems. ZDA poses a formidable security ...challenge since its attack signal is hidden in the null space of the state-space representation of the control system and hence it can evade conventional detection methods. An intuitive defense strategy builds on changing the aforementioned representation via switching through a set of carefully crafted topologies. In this article, we propose realistic ZDA variations where the attacker is aware of this topology-switching strategy, and hence employs the following policies to avoid detection: first, pause, update, and resume ZDA according to the knowledge of switching topologies; and second, cooperate with a concurrent stealthy topology attack that alters network topology at switching times, such that the original ZDA is feasible under the corrupted topology. We first systematically study the proposed ZDA variations, and then develop defense strategies against them under the realistic assumption that the defender has no knowledge of attack starting, pausing, and resuming times and the number of misbehaving agents. Particularly, we characterize conditions for detectability of the proposed ZDA variations, in terms of the network topologies to be maintained, the set of agents to be monitored, and the measurements of the monitored agents that should be extracted, while simultaneously preserving the privacy of the states of the nonmonitored agents. We then propose an attack detection algorithm based on the Luenberger observer, using the characterized detectability conditions. We provide numerical simulation results to demonstrate our theoretical findings.
We analyze in this paper finite horizon hierarchical signaling games between (information provider) senders and (decision maker) receivers in a dynamic environment. The underlying information evolves ...in time while sender and receiver interact repeatedly. Different from the classical communication (control) models, however, the sender (sensor) and the receiver (controller) have different objectives and there is a hierarchy between the players such that the sender leads the game by announcing his policies beforehand. He needs to anticipate the reaction of the receiver and the impact of the actions on the horizon while controlling the transparency of the disclosed information at each interaction. With quadratic cost functions and multivariate Gaussian processes, evolving according to first order auto-regressive models, we show that memoryless “linear” sender signaling rules are optimal (in the sense of game-theoretic hierarchical equilibrium) within the general class of measurable policies in the noncooperative communication context. In the noncooperative control context, we also analyze the hierarchical equilibrium for linear signaling rules and provide an algorithm to compute the optimal linear signaling rules numerically with global optimality guarantees.
This paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying ...memoryless stochastic process, and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon. The sensor is either charged a cost for each transmission or constrained on transmission times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. Under some technical assumptions, we obtain the optimal encoding and estimation policies within the piecewise affine class in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase-transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.
Path planning is an important component of autonomous mobile sensing systems. This paper studies upper and lower bounds of communication performance over Gaussian sensor networks, to drive ...power-distortion metrics for path planning problems. The Gaussian multiple-access channel is employed as a channel model and two source models are considered. In the first setting, the underlying source is estimated with minimum mean-squared-error, while in the second, reconstruction of a random spatial field is considered. For both problem settings, the upper and the lower bounds of sensor power-distortion curve are derived. For both settings, the upper bounds follow from the amplify-and-forward scheme and the lower bounds admit a unified derivation based on data processing inequality and tensorization property of the maximal correlation measure. Next, closed-form solutions of the optimal power allocation problems are obtained under a weighted sum-power constraint. The gap between the upper and the lower bounds is analyzed for both weighted sum and individual power constrained settings. Finally, these metrics are used to drive a path planning algorithm and the effects of power-distortion metrics, network parameters, and power optimization on the optimized path selection are analyzed.
This article studies topology inference, from agent states, of a directed cyber-social network with opinion spreading dynamics model that explicitly takes confirmation bias into account. The ...cyber-social network comprises a set of partially connected directed network of agents at the social level, and a set of information sources at the cyber layer. The necessary and sufficient conditions for the existence of exact inference solution are characterized. A method for exact inference, when it is possible, of entire network topology as well as confirmation bias model parameters is proposed for the case where the bias mentioned earlier follows a piece-wise linear model. The particular case of no confirmation bias is analyzed in detail. For the setting where the model of confirmation bias is unknown, an algorithm that approximates the network topology, building on the exact inference method, is presented. This algorithm can exactly infer the weighted communication from the neighbors to the non-followers of information sources. Numerical simulations demonstrate the effectiveness of the proposed methods for different scenarios.
This paper provides a model to investigate information spread over cyber-social network of agents. The cyber-social network considered here comprises individuals and information sources. Each ...individual holds an opinion represented by a scalar that evolves over time. The information sources are stubborn, in the sense that their opinions are time-invariant. Individuals receive the opinions of information sources that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of cyber-social networks is adopted from DeGroot-Friedkin model, where an individual's opinion update mechanism is a convex combination of her innate opinion, her neighbors' opinions at the previous time step (obtained from the social network), and the opinions passed along by information sources from cyber layer which she follows. The characteristics of the interdependent social and cyber networks are significantly different here: the social network relies on trust and hence static, while influences from information sources to individuals are highly dynamic since they are weighted as a function of the distance between an individual state and the state of information source to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium point are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of polarization in the opinions of information sources on the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.
This paper studies the problem of global optimization of zero-delay source-channel codes that map between the source space and the channel space, under a given transmission power constraint and for ...the mean-square-error distortion. Particularly, we focus on two well-known network settings: the Wyner-Ziv setting where only a decoder has access to side information and the distributed setting where independent encoders transmit over independent channels to a central decoder. Prior work derived the necessary conditions for optimality of the encoder and decoder mappings, along with a greedy optimization algorithm that imposes these conditions iteratively, in conjunction with the heuristic noisy channel relaxation method to mitigate poor local minima. While noisy channel relaxation is arguably effective in simple settings, it fails to provide accurate global optimization in more complicated settings considered in this paper. We propose a powerful nonconvex optimization method based on the concept of deterministic annealing-which is derived from information theoretic principles and was successfully employed in several problems including vector quantization, classification, and regression. We present comparative numerical results that show strict superiority of the proposed method over greedy optimization methods as well as prior approaches in literature.
This article investigates the impact of confirmation bias on competitive information spread in the social network that comprises individuals in a social network and competitive information sources at ...a cyber layer. We formulate the problem of information spread as a zero-sum game, which admits a unique Nash equilibrium in pure strategies. We characterize the dependence of pure Nash equilibrium on the public's innate opinions, the social network topology, as well as the parameters of confirmation bias. We uncover that confirmation bias moves the equilibrium toward the center only when the innate opinions are not neutral, and this move does not occur for the competitive information sources simultaneously. Numerical examples in the context of well-known Krackhardt's advice network are provided to demonstrate the correctness of theoretical results.
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