41 research outputs found
A Game-Theoretic Framework for Optimum Decision Fusion in the Presence of Byzantines
Optimum decision fusion in the presence of malicious nodes - often referred
to as Byzantines - is hindered by the necessity of exactly knowing the
statistical behavior of Byzantines. By focusing on a simple, yet widely
studied, set-up in which a Fusion Center (FC) is asked to make a binary
decision about a sequence of system states by relying on the possibly corrupted
decisions provided by local nodes, we propose a game-theoretic framework which
permits to exploit the superior performance provided by optimum decision
fusion, while limiting the amount of a-priori knowledge required. We first
derive the optimum decision strategy by assuming that the statistical behavior
of the Byzantines is known. Then we relax such an assumption by casting the
problem into a game-theoretic framework in which the FC tries to guess the
behavior of the Byzantines, which, in turn, must fix their corruption strategy
without knowing the guess made by the FC. We use numerical simulations to
derive the equilibrium of the game, thus identifying the optimum behavior for
both the FC and the Byzantines, and to evaluate the achievable performance at
the equilibrium. We analyze several different setups, showing that in all cases
the proposed solution permits to improve the accuracy of data fusion. We also
show that, in some instances, it is preferable for the Byzantines to minimize
the mutual information between the status of the observed system and the
reports submitted to the FC, rather than always flipping the decision made by
the local nodes as it is customarily assumed in previous works
A Message Passing Approach for Decision Fusion in Adversarial Multi-Sensor Networks
We consider a simple, yet widely studied, set-up in which a Fusion Center
(FC) is asked to make a binary decision about a sequence of system states by
relying on the possibly corrupted decisions provided by byzantine nodes, i.e.
nodes which deliberately alter the result of the local decision to induce an
error at the fusion center. When independent states are considered, the optimum
fusion rule over a batch of observations has already been derived, however its
complexity prevents its use in conjunction with large observation windows.
In this paper, we propose a near-optimal algorithm based on message passing
that greatly reduces the computational burden of the optimum fusion rule. In
addition, the proposed algorithm retains very good performance also in the case
of dependent system states. By first focusing on the case of small observation
windows, we use numerical simulations to show that the proposed scheme
introduces a negligible increase of the decision error probability compared to
the optimum fusion rule. We then analyse the performance of the new scheme when
the FC make its decision by relying on long observation windows. We do so by
considering both the case of independent and Markovian system states and show
that the obtained performance are superior to those obtained with prior
suboptimal schemes. As an additional result, we confirm the previous finding
that, in some cases, it is preferable for the byzantine nodes to minimise the
mutual information between the sequence system states and the reports submitted
to the FC, rather than always flipping the local decision
On Noise-Enhanced Distributed Inference in the Presence of Byzantines
This paper considers the noise-enhanced distributed detection problem in the presence of Byzantine (malicious) nodes by suitably adding stochastic resonance (SR) noise. We consider two metrics - the minimum number of Byzantines (alpha_blind) needed to blind the fusion center as a security metric and the Kullback- Leibler divergence (DKL) as a detection performance metric. We show that alpha_blind increases when SR noise is added at the honest nodes. When Byzantines also start adding SR noise to their observations, we see no gain in terms of alpha_blind . However, the detection performance of the network does improve with SR. We also consider a game theoretic formulation where this problem of distributed detection in the presence of Byzantines is modeled as a minimax game between the Byzantines and the inference network, and numerically find Nash equilibria. The case when SR noise is added to the signals received at the fusion center (FC) from the sensors is also considered. Our numerical results indicate that while there is no gain in terms of , the network-wide performance measured in terms of alpha_blind the deflection coefficient does improve in this cas
Integrating Human Decisions in the Presence of Byzantines: An Evolutionary Game Theoretical Approach
Reliable Inference from Unreliable Agents
Distributed inference using multiple sensors has been an active area of research since the emergence of wireless sensor networks (WSNs). Several researchers have addressed the design issues to ensure optimal inference performance in such networks. The central goal of this thesis is to analyze distributed inference systems with potentially unreliable components and design strategies to ensure reliable inference in such systems. The inference process can be that of detection or estimation or classification, and the components/agents in the system can be sensors and/or humans. The system components can be unreliable due to a variety of reasons: faulty sensors, security attacks causing sensors to send falsified information, or unskilled human workers sending imperfect information. This thesis first quantifies the effect of such unreliable agents on the inference performance of the network and then designs schemes that ensure a reliable overall inference.
In the first part of this thesis, we study the case when only sensors are present in the system, referred to as sensor networks. For sensor networks, the presence of malicious sensors, referred to as Byzantines, are considered. Byzantines are sensors that inject false information into the system. In such systems, the effect of Byzantines on the overall inference performance is characterized in terms of the optimal attack strategies. Game-theoretic formulations are explored to analyze two-player interactions.
Next, Byzantine mitigation schemes are designed that address the problem from the system\u27s perspective. These mitigation schemes are of two kinds: Byzantine identification schemes and Byzantine tolerant schemes. Using learning based techniques, Byzantine identification schemes are designed that learn the identity of Byzantines in the network and use this information to improve system performance. When such schemes are not possible, Byzantine tolerant schemes using error-correcting codes are developed that tolerate the effect of Byzantines and maintain good performance in the network. Error-correcting codes help in correcting the erroneous information from these Byzantines and thereby counter their attack.
The second line of research in this thesis considers humans-only networks, referred to as human networks. A similar research strategy is adopted for human networks where, the effect of unskilled humans sharing beliefs with a central observer called \emph{CEO} is analyzed, and the loss in performance due to the presence of such unskilled humans is characterized. This problem falls under the family of problems in information theory literature referred to as the \emph{CEO Problem}, but for belief sharing. The asymptotic behavior of the minimum achievable mean squared error distortion at the CEO is studied in the limit when the number of agents and the sum rate tend to infinity.
An intermediate regime of performance between the exponential behavior in discrete CEO problems and the
behavior in Gaussian CEO problems is established. This result can be summarized as the fact that sharing beliefs (uniform) is fundamentally easier in terms of convergence rate than sharing measurements (Gaussian), but sharing decisions is even easier (discrete).
Besides theoretical analysis, experimental results are reported for experiments designed in collaboration with cognitive psychologists to understand the behavior of humans in the network. The act of fusing decisions from multiple agents is observed for humans and the behavior is statistically modeled using hierarchical Bayesian models. The implications of such modeling on the design of large human-machine systems is discussed. Furthermore, an error-correcting codes based scheme is proposed to improve system performance in the presence of unreliable humans in the inference process. For a crowdsourcing system consisting of unskilled human workers providing unreliable responses, the scheme helps in designing easy-to-perform tasks and also mitigates the effect of erroneous data. The benefits of using the proposed approach in comparison to the majority voting based approach are highlighted using simulated and real datasets.
In the final part of the thesis, a human-machine inference framework is developed where humans and machines interact to perform complex tasks in a faster and more efficient manner. A mathematical framework is built to understand the benefits of human-machine collaboration. Such a study is extremely important for current scenarios where humans and machines are constantly interacting with each other to perform even the simplest of tasks. While machines perform best in some tasks, humans still give better results in tasks such as identifying new patterns. By using humans and machines together, one can extract complete information about a phenomenon of interest. Such an architecture, referred to as Human-Machine Inference Networks (HuMaINs), provides promising results for the two cases of human-machine collaboration: \emph{machine as a coach} and \emph{machine as a colleague}. For simple systems, we demonstrate tangible performance gains by such a collaboration which provides design modules for larger, and more complex human-machine systems. However, the details of such larger systems needs to be further explored
Distributed Inference and Learning with Byzantine Data
We are living in an increasingly networked world with sensing networks of varying shapes and sizes: the network often comprises of several tiny devices (or nodes) communicating with each other via different topologies. To make the problem even more complicated, the nodes in the network can be unreliable due to a variety of reasons: noise, faults and attacks, thus, providing
corrupted data. Although the area of statistical inference has been an active area of research in the
past, distributed learning and inference in a networked setup with potentially unreliable components
has only gained attention recently. The emergence of big and dirty data era demands new
distributed learning and inference solutions to tackle the problem of inference with corrupted data.
Distributed inference networks (DINs) consist of a group of networked entities which acquire
observations regarding a phenomenon of interest (POI), collaborate with other entities in the network
by sharing their inference via different topologies to make a global inference. The central
goal of this thesis is to analyze the effect of corrupted (or falsified) data on the inference performance
of DINs and design robust strategies to ensure reliable overall performance for several
practical network architectures. Specifically, the inference (or learning) process can be that of detection
or estimation or classification, and the topology of the system can be parallel, hierarchical
or fully decentralized (peer to peer).
Note that, the corrupted data model may seem similar to the scenario where local decisions
are transmitted over a Binary Symmetric Channel (BSC) with a certain cross over probability,
however, there are fundamental differences. Over the last three decades, research community
has extensively studied the impact of transmission channels or faults on the distributed detection
system and related problems due to its importance in several applications. However, corrupted
(Byzantine) data models considered in this thesis, are philosophically different from the BSC or
the faulty sensor cases. Byzantines are intentional and intelligent, therefore, they can optimize
over the data corruption parameters. Thus, in contrast to channel aware detection, both the FC and
the Byzantines can optimize their utility by choosing their actions based on the knowledge of their
opponent’s behavior. Study of these practically motivated scenarios in the presence of Byzantines
is of utmost importance, and is missing from the channel aware detection and fault tolerant detection
literature. This thesis advances the distributed inference literature by providing fundamental
limits of distributed inference with Byzantine data and provides optimal counter-measures (using
the insights provided by these fundamental limits) from a network designer’s perspective. Note
that, the analysis of problems related to strategical interaction between Byzantines and network
designed is very challenging (NP-hard is many cases). However, we show that by utilizing the
properties of the network architecture, efficient solutions can be obtained. Specifically, we found
that several problems related to the design of optimal counter-measures in the inference context
are, in fact, special cases of these NP-hard problems which can be solved in polynomial time.
First, we consider the problem of distributed Bayesian detection in the presence of data falsification
(or Byzantine) attacks in the parallel topology. Byzantines considered in this thesis are those
nodes that are compromised and reprogrammed by an adversary to transmit false information to
a centralized fusion center (FC) to degrade detection performance. We show that above a certain
fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable
(or blind) of utilizing the sensor data for detection. When the fraction of Byzantines is not
sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies
for the Byzantines that most degrade the detection performance. Optimal attacking strategies
in certain cases have the minimax property and, therefore, the knowledge of these strategies has
practical significance and can be used to implement a robust detector at the FC.
In several practical situations, parallel topology cannot be implemented due to limiting factors,
such as, the FC being outside the communication range of the nodes and limited energy budget of
the nodes. In such scenarios, a multi-hop network is employed, where nodes are organized hierarchically
into multiple levels (tree networks). Next, we study the problem of distributed inference
in tree topologies in the presence of Byzantines under several practical scenarios. We analytically
characterize the effect of Byzantines on the inference performance of the system. We also look at
the possible counter-measures from the FC’s perspective to protect the network from these Byzantines.
These counter-measures are of two kinds: Byzantine identification schemes and Byzantine
tolerant schemes. Using learning based techniques, Byzantine identification schemes are designed
that learn the identity of Byzantines in the network and use this information to improve system
performance. For scenarios where this is not possible, Byzantine tolerant schemes, which use
game theory and error-correcting codes, are developed that tolerate the effect of Byzantines while
maintaining a reasonably good inference performance in the network.
Going a step further, we also consider scenarios where a centralized FC is not available. In
such scenarios, a solution is to employ detection approaches which are based on fully distributed
consensus algorithms, where all of the nodes exchange information only with their neighbors. For
such networks, we analytically characterize the negative effect of Byzantines on the steady-state
and transient detection performance of conventional consensus-based detection schemes. To avoid
performance deterioration, we propose a distributed weighted average consensus algorithm that is
robust to Byzantine attacks. Next, we exploit the statistical distribution of the nodes’ data to devise
techniques for mitigating the influence of data falsifying Byzantines on the distributed detection
system. Since some parameters of the statistical distribution of the nodes’ data might not be known
a priori, we propose learning based techniques to enable an adaptive design of the local fusion or
update rules.
The above considerations highlight the negative effect of the corrupted data on the inference
performance. However, it is possible for a system designer to utilize the corrupted data for network’s
benefit. Finally, we consider the problem of detecting a high dimensional signal based on
compressed measurements with secrecy guarantees. We consider a scenario where the network
operates in the presence of an eavesdropper who wants to discover the state of the nature being
monitored by the system. To keep the data secret from the eavesdropper, we propose to use cooperating
trustworthy nodes that assist the FC by injecting corrupted data in the system to deceive the
eavesdropper. We also design the system by determining the optimal values of parameters which
maximize the detection performance at the FC while ensuring perfect secrecy at the eavesdropper
Byzantine Attack and Defense in Cognitive Radio Networks: A Survey
The Byzantine attack in cooperative spectrum sensing (CSS), also known as the
spectrum sensing data falsification (SSDF) attack in the literature, is one of
the key adversaries to the success of cognitive radio networks (CRNs). In the
past couple of years, the research on the Byzantine attack and defense
strategies has gained worldwide increasing attention. In this paper, we provide
a comprehensive survey and tutorial on the recent advances in the Byzantine
attack and defense for CSS in CRNs. Specifically, we first briefly present the
preliminaries of CSS for general readers, including signal detection
techniques, hypothesis testing, and data fusion. Second, we analyze the spear
and shield relation between Byzantine attack and defense from three aspects:
the vulnerability of CSS to attack, the obstacles in CSS to defense, and the
games between attack and defense. Then, we propose a taxonomy of the existing
Byzantine attack behaviors and elaborate on the corresponding attack
parameters, which determine where, who, how, and when to launch attacks. Next,
from the perspectives of homogeneous or heterogeneous scenarios, we classify
the existing defense algorithms, and provide an in-depth tutorial on the
state-of-the-art Byzantine defense schemes, commonly known as robust or secure
CSS in the literature. Furthermore, we highlight the unsolved research
challenges and depict the future research directions.Comment: Accepted by IEEE Communications Surveys and Tutoiral
Cyber-Physical Security Strategies
Cyber-physical security describes the protection of systems with close relationships between computational functions and physical ones and addresses the issue of vulnerability to attack through both cyber and physical avenues. This describes systems in a wide variety of functions, many crucial to the function of modern society, making their security of paramount importance. The development of secure system design and attack detection strategies for each potential avenue of attack is needed to combat malicious attacks. This thesis will provide an overview of the approaches to securing different aspect of cyber-physical systems. The cyber element can be designed to better prevent unauthorized entry and to be more robust to attack while its use is evaluated for signs of ongoing intrusion. Nodes in sensor networks can be evaluated by their claims to determine the likelihood of their honesty. Control systems can be designed to be robust in cases of the failure of one component and to detect signal insertion or replay attack. Through the application of these strategies, the safety and continued function of cyber-physical systems can be improved