Optimal distributed detection in the presence of Byzantines
Swastik Brahma2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing
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Abstract
This paper considers the problem of optimal distributed detection with independent identical sensors in the presence of Byzantine attacks. By considering the attacker to be strategic in nature, we address the issue of designing the optimal fusion rule and the local sensor thresholds that minimize the probability of error at the fusion center (FC). We first consider the problem of finding the optimal fusion rule under the constraint of fixed local sensor thresholds and fixed Byzantine strategy. Next, we consider the problem of joint optimization of the fusion rule and local sensor thresholds for a fixed Byzantine strategy. Then we extend these results to the scenario where both the FC and the Byzantine attacker act in a strategic manner to optimize their own utilities. We model the strategic behavior of the FC and the attacker using game theory and show the existence of Nash Equilibrium. We also provide numerical results to gain insights into the solution.
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Basic Notions of Distributed Detection, Information Fusion and Game Theory
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Distributed sensor networks consist of a set of spatially distributed sensors that operate as data collectors or decision makers to monitor a shared phenomenon. This is a common case in many real world situations like air-traffic control, economic and finance, medical diagnosis, electric power networks, wireless sensor networks, cognitive radio networks, online reputation systems, and many others. Usually, in centralized networks, if there are no power, channel, communication or privacy constraints, the sensors can send the full raw information they collect to a FC. However, real life situations are different and several constraints must be considered e.g. when sensors are spatially distributed over a large territorial area, when the channel bandwidth is limited, or even when the sensors are supplied with short life power sources. To address these limitations, sensors must perform some local processing before sending a compressed version of the collected information to the FC. The abstraction level of the information summary can vary a lot. For instance, it can be a quantized set of the raw information, a soft summary statistic like an average or a likelihood value, or even a single information bit. By means of a fusion rule, the FC integrates the information received from the sensors to make a global decision regarding the system or phenomena under observation. The definition of the fusion rule depends on the a-priori information available about the sensors, the transmission channel and the phenomena as well as the type of information provided by the sensors. Fusion rules can be as simple as voting rules or sophisticated statistical rules. Since the behavior of the sensors in the networks could be different due to noise or intentional acts, the interplay between the sensors or between them and the FC could be modeled using Game Theory, which is a mathematical field that studies the situations of competition and/or cooperation, between decision makers or agents. This chapter is divided into two parts. In the first part, we briefly introduce some basic notions of detection theory and outline some detection techniques used locally
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IEEE Transactions on Information Forensics and Security, 2015
In this paper, the problem of distributed detection in tree networks in the presence of Byzantines is considered. Closed form expressions for optimal attacking strategies that minimize the miss detection error exponent at the fusion center (FC) are obtained. We also look at the problem from the network designer's (FC's) perspective. We study the problem of designing optimal distributed detection parameters in a tree network in the presence of Byzantines. Next, we model the strategic interaction between the FC and the attacker as a Leader-Follower (Stackelberg) game. This formulation provides a methodology for predicting attacker and defender (FC) equilibrium strategies, which can be used to implement the optimal detector. Finally, a reputation based scheme to identify Byzantines is proposed and its performance is analytically evaluated. We also provide some numerical examples to gain insights into the solution.
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