arXiv subjects

Shreyas Sundaram

Publications and source records attributed to Shreyas Sundaram.

At least 55 records · Page 3Linked to original sources

arXiv2021

On the Computational Complexity of the Secure State-Reconstruction Problem

In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard. We then introduce the notion of eigenvalue observability and show that the state can be reconstructed in polynomial time when each eigenvalue is observable by at least $2s+1$ sensors and at most $s$ sensors are corrupted by an adversary. However, there is a gap between eigenvalue observability and the possibility of reconstructing the state despite attacks - this gap has been characterized in the literature by the notion of sparse observability. To better understand this, we show that when the $\mathbf{A}$ matrix of the linear system has unitary geometric multiplicity, the gap disappears, i.e., eigenvalue observability coincides with sparse observability, and there exists a polynomial time algorithm to reconstruct the state provided the state can be reconstructed.

eess.SY↗

arXiv2021

Distributed Inference with Sparse and Quantized Communication

We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just $1$ bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.

eess.SY↗

arXiv2021

Parameter Estimation in Epidemic Spread Networks Using Limited Measurements

We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.

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arXiv2021

Near-Optimal Data Source Selection for Bayesian Learning

We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First, we show that the data source selection problem for Bayesian learning is NP-hard. We then show that the data source selection problem can be transformed into an instance of the submodular set covering problem studied in the literature, and provide a standard greedy algorithm to solve the data source selection problem with provable performance guarantees. Next, we propose a fast greedy algorithm that improves the running times of the standard greedy algorithm, while achieving performance guarantees that are comparable to those of the standard greedy algorithm. The fast greedy algorithm can also be applied to solve the general submodular set covering problem with performance guarantees. Finally, we validate the theoretical results using numerical examples, and show that the greedy algorithms work well in practice.

cs.LG↗

arXiv2021

Towards Resilience for Multi-Agent $QD$-Learning

This paper considers the multi-agent reinforcement learning (MARL) problem for a networked (peer-to-peer) system in the presence of Byzantine agents. We build on an existing distributed $Q$-learning algorithm, and allow certain agents in the network to behave in an arbitrary and adversarial manner (as captured by the Byzantine attack model). Under the proposed algorithm, if the network topology is $(2F+1)$-robust and up to $F$ Byzantine agents exist in the neighborhood of each regular agent, we establish the almost sure convergence of all regular agents' value functions to the neighborhood of the optimal value function of all regular agents. For each state, if the optimal $Q$-values of all regular agents corresponding to different actions are sufficiently separated, our approach allows each regular agent to learn the optimal policy for all regular agents.

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arXiv2021

The Effect of Behavioral Probability Weighting in a Simultaneous Multi-Target Attacker-Defender Game

We consider a security game in a setting consisting of two players (an attacker and a defender), each with a given budget to allocate towards attack and defense, respectively, of a set of nodes. Each node has a certain value to the attacker and the defender, along with a probability of being successfully compromised, which is a function of the investments in that node by both players. For such games, we characterize the optimal investment strategies by the players at the (unique) Nash Equilibrium. We then investigate the impacts of behavioral probability weighting on the investment strategies; such probability weighting, where humans overweight low probabilities and underweight high probabilities, has been identified by behavioral economists to be a common feature of human decision-making. We show via numerical experiments that behavioral decision-making by the defender causes the Nash Equilibrium investments in each node to change (where the defender overinvests in the high-value nodes and underinvests in the low-value nodes).

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arXiv2020

Combining Hybrid Input-Output Automaton and Game Theory for Security Modeling of Cyber-Physical Systems

We consider a security setting in which the Cyber-Physical System (CPS) is composed of subnetworks where each subnetwork is under ownership of one defender. Such CPS can be represented by an attack graph where the defenders are required to invest (subject to a budget constraint) on the graph's edges in order to protect their critical assets (where each defender's critical asset has a certain value to the defender if compromised). We model such CPS using Hybrid Input-Output Automaton (HIOA) where each subnetwork is represented by a HIOA module. We first establish the building blocks needed in our setting. We then present our model that characterizes the continuous time evolution of the investments and discrete transitions between different states (where each state represents different condition and/or perturbation) within the system. Finally, we provide a real-world CPS example to validate our modeling.

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arXiv2020

Algorithms for Influence Maximization in Socio-Physical Networks

Given a directed graph (representing a social network), the influence maximization problem is to find k nodes which, when influenced (or activated), would maximize the number of remaining nodes that get activated. In this paper, we consider a more general version of the problem that includes an additional set of nodes, termed as physical nodes, such that a node in the social network is covered by one or more physical nodes. A physical node exists in one of two states at any time, opened or closed, and there is a constraint on the maximum number of physical nodes that can be opened. In this setting, an inactive node in the social network becomes active if it has enough active neighbors in the social network and if it is covered by at least one of the opened physical nodes. This problem arises in disaster recovery, where a displaced social group decides to return after a disaster only after enough groups in its social network return and some infrastructure components in its neighborhood are repaired. The general problem is NP-hard to approximate within any constant factor and thus we characterize optimal and approximation algorithms for special instances of the problem.

cs.SI↗

arXiv2020

Morshed: Guiding Behavioral Decision-Makers towards Better Security Investment in Interdependent Systems

We model the behavioral biases of human decision-making in securing interdependent systems and show that such behavioral decision-making leads to a suboptimal pattern of resource allocation compared to non-behavioral (rational) decision-making. We provide empirical evidence for the existence of such behavioral bias model through a controlled subject study with 145 participants. We then propose three learning techniques for enhancing decision-making in multi-round setups. We illustrate the benefits of our decision-making model through multiple interdependent real-world systems and quantify the level of gain compared to the case in which the defenders are behavioral. We also show the benefit of our learning techniques against different attack models. We identify the effects of different system parameters on the degree of suboptimality of security outcomes due to behavioral decision-making.

cs.CR↗

arXiv2020

Policies for Multi-Agency Recovery of Physical Infrastructure After Disasters

We consider a scenario where multiple infrastructure components have been damaged after a disaster and the health value of each component continues to deteriorate if it is not being targeted by a repair agency, until it fails irreversibly. There are multiple agencies that seek to repair the components and there is an authority whose task is to allocate the components to the agencies within a given budget, so that the total number of components that are fully repaired by the agencies is maximized. We characterize the optimal policy for allocation and repair sequencing when the repair rates are sufficiently larger than the deterioration rates. For the case when the deterioration rates are larger than or equal to the repair rates, the rates are homogeneous across the components, and the costs charged by the entities for repair are equal, we characterize a policy for allocation and repair sequencing that permanently repairs at least half the number of components as that by an optimal policy.

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arXiv2020

Distributed Maximization of Submodular and Approximately Submodular Functions

We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a near-optimal solution to the global maximization problem using only local information and communication with neighbors in the graph. The near-optimal solution approaches the (1-1/e) approximation of the optimal solution to the global maximization problem with an additive factor that depends on the number of communication steps in the algorithm. We then analyze convergence guarantees of the proposed algorithm. This analysis reveals a tradeoff between the number of communication steps and the performance of the algorithm. Finally, we extend our analysis to nonsubmodular settings, using the notion of approximate submodularity.

math.OC↗

arXiv2020

Control Policies for Recovery of Interdependent Systems After Disruptions

We examine a control problem where the states of the components of a system deteriorate after a disruption, if they are not being repaired by an entity. There exist a set of dependencies in the form of precedence constraints between the components, captured by a directed acyclic graph (DAG). The objective of the entity is to maximize the number of components whose states are brought back to the fully repaired state within a given time. We prove that the general problem is NP-hard, and therefore we characterize near-optimal control policies for special instances of the problem. We show that when the deterioration rates are larger than or equal to the repair rates and the precedence constraints are given by a DAG, it is optimal to continue repairing a component until its state reaches the fully recovered state before switching to repair any other component. Under the aforementioned assumptions and when the deterioration and the repair rates are homogeneous across all the components, we prove that the control policy that targets the healthiest component at each time-step while respecting the precedence and time constraints fully repairs at least half the number of components that would be fully repaired by an optimal policy. Finally, we prove that when the repair rates are sufficiently larger than the deterioration rates, the precedence constraints are given by a set of disjoint trees that each contain at most k nodes, and there is no time constraint, the policy that targets the component with the least value of health minus the deterioration rate at each time-step while respecting the precedence constraints fully repairs at least 1/k times the number of components that would be fully repaired by an optimal policy.

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arXiv2020

On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly.

math.OC↗

arXiv2020

Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design-time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial-time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudo-polynomial-time algorithm to solve it.

math.OC↗

arXiv2020

Behavioral and Game-Theoretic Security Investments in Interdependent Systems Modeled by Attack Graphs

We consider a system consisting of multiple interdependent assets, and a set of defenders, each responsible for securing a subset of the assets against an attacker. The interdependencies between the assets are captured by an attack graph, where an edge from one asset to another indicates that if the former asset is compromised, an attack can be launched on the latter asset. Each edge has an associated probability of successful attack, which can be reduced via security investments by the defenders. In such scenarios, we investigate the security investments that arise under certain features of human decision-making that have been identified in behavioral economics. In particular, humans have been shown to perceive probabilities in a nonlinear manner, typically overweighting low probabilities and underweighting high probabilities. We show that suboptimal investments can arise under such weighting in certain network topologies. We also show that pure strategy Nash equilibria exist in settings with multiple (behavioral) defenders, and study the inefficiency of the equilibrium investments by behavioral defenders compared to a centralized socially optimal solution.

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arXiv2020

Optimal Policies for Recovery of Multiple Systems After Disruptions

We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we consider the problem of finding an optimal control (or switching) sequence to maximize the sum of the weights of the components whose states are brought back to the maximum value. We first provide several characteristics of the optimal policy for the general (fully heterogeneous) version of this problem. We then show that under certain conditions on the rates of repair and deterioration, we can explicitly characterize the optimal control policy as a function of the states. When the deterioration rate (when not being repaired) is larger than or equal to the repair rate, and the deterioration and repair rates as well as the weights are homogeneous across all the components, the optimal control policy is to target the component that has the largest state value at each time step. On the other hand, if the repair rates are sufficiently larger than the deterioration rates, the optimal control policy is to target the component whose state minus the deterioration rate is least in a particular subset of components at each time step.

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arXiv2020

BASCPS: How does behavioral decision making impact the security of cyber-physical systems?

We study the security of large-scale cyber-physical systems (CPS) consisting of multiple interdependent subsystems, each managed by a different defender. Defenders invest their security budgets with the goal of thwarting the spread of cyber attacks to their critical assets. We model the security investment decisions made by the defenders as a security game. While prior work has used security games to analyze such scenarios, we propose behavioral security games, in which defenders exhibit characteristics of human decision making that have been identified in behavioral economics as representing typical human cognitive biases. This is important as many of the critical security decisions in our target class of systems are made by humans. We provide empirical evidence for our behavioral model through a controlled subject experiment. We then show that behavioral decision making leads to a suboptimal pattern of resource allocation compared to non-behavioral decision making. We illustrate the effects of behavioral decision making using two representative real-world interdependent CPS. In particular, we identify the effects of the defenders' security budget availability and distribution, the degree of interdependency among defenders, and collaborative defense strategies, on the degree of suboptimality of security outcomes due to behavioral decision making. In this context, the adverse effects of behavioral decision making are most severe with moderate defense budgets. Moreover, the impact of behavioral suboptimal decision making is magnified as the degree of the interdependency between subnetworks belonging to different defenders increases. We also observe that selfish defense decisions together with behavioral decisions significantly increase security risk.

cs.CR↗

arXiv2020

Controlling Human Utilization of Failure-Prone Systems via Taxes

We consider a game-theoretic model where individuals compete over a shared failure-prone system or resource. We investigate the effectiveness of a taxation mechanism in controlling the utilization of the resource at the Nash equilibrium when the decision-makers have behavioral risk preferences, captured by prospect theory. We first observe that heterogeneous prospect-theoretic risk preferences can lead to counter-intuitive outcomes. In particular, for resources that exhibit network effects, utilization can increase under taxation and there may not exist a tax rate that achieves the socially optimal level of utilization. We identify conditions under which utilization is monotone and continuous, and then characterize the range of utilizations that can be achieved by a suitable choice of tax rate. We further show that resource utilization is higher when players are charged differentiated tax rates compared to the case when all players are charged an identical tax rate, under suitable assumptions.

cs.GT↗