arXiv subjects

Cedric Langbort

Publications and source records attributed to Cedric Langbort.

31 records · Page 2Linked to original sources

arXiv2017

Optimal Communication Strategies in Networked Cyber-Physical Systems with Adversarial Elements

This paper studies optimal communication and coordination strategies in cyber-physical systems for both defender and attacker within a game-theoretic framework. We model the communication network of a cyber-physical system as a sensor network which involves one single Gaussian source observed by many sensors, subject to additive independent Gaussian observation noises. The sensors communicate with the estimator over a coherent Gaussian multiple access channel. The aim of the receiver is to reconstruct the underlying source with minimum mean squared error. The scenario of interest here is one where some of the sensors are captured by the attacker and they act as the adversary (jammer): they strive to maximize distortion. The receiver (estimator) knows the captured sensors but still cannot simply ignore them due to the multiple access channel, i.e., the outputs of all sensors are summed to generate the estimator input. We show that the ability of transmitter sensors to secretly agree on a random event, that is "coordination", plays a key role in the analysis...

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arXiv2016

Convergence Analysis of Iterated Best Response for a Trusted Computation Game

We introduce a game of trusted computation in which a sensor equipped with limited computing power leverages a central node to evaluate a specified function over a large dataset, collected over time. We assume that the central computer can be under attack and we propose a strategy where the sensor retains a limited amount of the data to counteract the effect of attack. We formulate the problem as a two player game in which the sensor (defender) chooses an optimal fusion strategy using both the non-trusted output from the central computer and locally stored trusted data. The attacker seeks to compromise the computation by influencing the fused value through malicious manipulation of the data stored on the central node. We first characterize all Nash equilibria of this game, which turn out to be dependent on parameters known to both players. Next we adopt an Iterated Best Response (IBR) scheme in which, at each iteration, the central computer reveals its output to the sensor, who then computes its best response based on a linear combination of its private local estimate and the untrusted third-party output. We characterize necessary and sufficient conditions for convergence of the IBR along with numerical results which show that the convergence conditions are relatively tight.

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arXiv2016

Price of Transparency in Strategic Machine Learning

Based on the observation that the transparency of an algorithm comes with a cost for the algorithm designer when the users (data providers) are strategic, this paper studies the impact of strategic intent of the users on the design and performance of transparent ML algorithms. We quantitatively study the {\bf price of transparency} in the context of strategic classification algorithms, by modeling the problem as a nonzero-sum game between the users and the algorithm designer. The cost of having a transparent algorithm is measured by a quantity, named here as price of transparency which is the ratio of the designer cost at the Stackelberg equilibrium, when the algorithm is transparent (which allows users to be strategic) to that of the setting where the algorithm is not transparent.

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arXiv2016

Detection of Biasing Attacks on Distributed Estimation Networks

The paper addresses the problem of detecting attacks on distributed estimator networks that aim to intentionally bias process estimates produced by the network. It provides a sufficient condition, in terms of the feasibility of certain linear matrix inequalities, which guarantees distributed input attack detection using an $H_\infty$ approach.

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arXiv2016

Scalar Quadratic-Gaussian Soft Watermarking Games

We introduce the zero-sum game problem of soft watermarking: The hidden information (watermark) comes from a continuum and has a perceptual value; the receiver generates an estimate of the embedded watermark to minimize the expected estimation error (unlike the conventional watermarking schemes where both the hidden information and the receiver output are from a discrete finite set). Applications include embedding a multimedia content into another. We consider in this paper the scalar Gaussian case and use expected mean-squared distortion. We formulate the resulting problem as a zero-sum game between the encoder & receiver pair and the attacker. We show that for the lin- ear encoder, the optimal attacker is Gaussian-affine, derive the optimal system parameters in that case, and discuss the corresponding system behavior. We also provide numerical results to gain further insight and understanding of the system behavior at optimality.

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arXiv2016

Information-Theoretic Approach to Strategic Communication as a Hierarchical Game

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 the structure of optimal strategies are identified. Finally, an extension of the results to the broader context of decentralized stochastic control is presented.

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arXiv2016

On the Role of Side Information In Strategic Communication

This paper analyzes the fundamental limits of strate- gic communication in network settings. Strategic communication differs from the conventional communication paradigms in in- formation theory since it involves different objectives for the encoder and the decoder, which are aware of this mismatch and act accordingly. This leads to a Stackelberg game where both agents commit to their mappings ex-ante. Building on our prior work on the point-to-point setting, this paper studies the compression and communication problems with the receiver and/or transmitter side information setting. The equilibrium strategies and associated costs are characterized for the Gaussian variables with quadratic cost functions. Several questions on the benefit of side information in source and joint source-channel coding in such strategic settings are analyzed. Our analysis has uncovered an interesting result on optimality of uncoded mappings in strategic source-channel coding in networks.

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arXiv2015

Privacy Constrained Information Processing

This paper studies communication scenarios where the transmitter and the receiver have different objectives due to privacy concerns, in the context of a variation of the strategic information transfer (SIT) model of Sobel and Crawford. We first formulate the problem as the minimization of a common distortion by the transmitter and the receiver subject to a privacy constrained transmitter. We show the equivalence of this formulation to a Stackelberg equilibrium of the SIT problem. Assuming an entropy based privacy measure, a quadratic distortion measure and jointly Gaussian variables, we characterize the Stackelberg equilibrium. Next, we consider asymptotically optimal compression at the transmitter which inherently provides some level of privacy, and study equilibrium conditions. We finally analyze the impact of the presence of an average power constrained Gaussian communication channel between the transmitter and the receiver on the equilibrium conditions.

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arXiv2015

Estimation with Strategic Sensors

We introduce a model of estimation in the presence of strategic, self-interested sensors. We employ a game-theoretic setup to model the interaction between the sensors and the receiver. The cost function of the receiver is equal to the estimation error variance while the cost function of the sensor contains an extra term which is determined by its private information. We start by the single sensor case in which the receiver has access to a noisy but honest side information in addition to the message transmitted by a strategic sensor. We study both static and dynamic estimation problems. For both these problems, we characterize a family of equilibria in which the sensor and the receiver employ simple strategies. Interestingly, for the dynamic estimation problem, we find an equilibrium for which the strategic sensor uses a memory-less policy. We generalize the static estimation setup to multiple sensors with synchronous communication structure (i.e., all the sensors transmit their messages simultaneously). We prove the maybe surprising fact that, for the constructed equilibrium in affine strategies, the estimation quality degrades as the number of sensors increases. However, if the sensors are herding (i.e., copying each other policies), the quality of the receiver's estimation improves as the number of sensors increases. Finally, we consider the asynchronous communication structure (i.e., the sensors transmit their messages sequentially).

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arXiv2014

On the Existence of Optimal Policies for a Class of Static and Sequential Dynamic Teams

In this paper, we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team-optimal solutions. We first investigate the existence of optimal solutions in static teams where the observations of the decision makers are conditionally independent or satisfy certain regularity conditions. Building on these findings and the static reduction method of Witsenhausen, we then extend the analysis to sequential dynamic teams. In particular, we show that a large class of dynamic LQG team problems, including the vector version of the well-known Witsenhausen's counterexample and the Gaussian relay channel problem viewed as a dynamic team, admit team-optimal solutions. Results in this paper substantially broaden the class of stochastic control and team problems with non-classical information known to have optimal solutions.

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arXiv2014

Common Information based Markov Perfect Equilibria for Linear-Gaussian Games with Asymmetric Information

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic information about the state process and the other controller's past actions and observations. This leads to a dynamic game of asymmetric information among the controllers. Building on our earlier work on finite games with asymmetric information, we devise an algorithm to compute a Nash equilibrium by using the common information among the controllers. We call such equilibria common information based Markov perfect equilibria of the game, which can be viewed as a refinement of Nash equilibrium in games with asymmetric information. If the players' cost functions are quadratic, then we show that under certain conditions a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. We also show through an example that there could be other Nash equilibria in a game of asymmetric information, not corresponding to common information based Markov perfect equilibria.

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arXiv2014

On Endogenous Random Consensus and Averaging Dynamics

Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, i.e.\ an averaging dynamics whose evolution suffers from history dependent sources of randomness. We show that under general assumptions on the averaging dynamics, such dynamics is convergent almost surely. We also determine the limiting behavior of such dynamics and show such dynamics admit infinitely many time-varying Lyapunov functions.

math.OC↗

arXiv2012

Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Lastly, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

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