44 research outputs found
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
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
Distributed Detection in Tree Networks: Byzantines and Mitigation Techniques
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