arXiv subjects

Jeff S. Shamma

Publications and source records attributed to Jeff S. Shamma.

At least 37 records · Page 2Linked to original sources

arXiv2019

Smart Jammer and LTE Network Strategies in An Infinite-Horizon Zero-Sum Repeated Game with Asymmetric and Incomplete Information

LTE/LTE-Advanced networks are known to be vulnerable to denial-of-service and loss-of-service attacks from smart jammers. In this article, the interaction between a smart jammer and LTE network is modeled as an infinite-horizon, zero-sum, asymmetric repeated game. The smart jammer and eNode B are modeled as the informed and the uninformed player, respectively. The main purpose of this article is to construct efficient suboptimal strategies for both players that can be used to solve the above-mentioned infinite-horizon repeated game with asymmetric and incomplete information. It has been shown in game-theoretic literature that security strategies provide optimal solution in zero-sum games. It is also shown that both players' security strategies in an infinite-horizon asymmetric game depend only on the history of the informed player's actions. However, fixed-sized sufficient statistics are needed for both players to solve the above-mentioned game efficiently. The smart jammer uses its evolving belief state as the fixed-sized sufficient statistics for the repeated game. Whereas, the LTE network (uninformed player) uses worst-case regret of its security strategy and its anti-discounted update as the fixed-sized sufficient statistics. Although fixed-sized sufficient statistics are employed by both players, optimal security strategy computation in λ-discounted asymmetric games is still hard to perform because of non-convexity. Hence, the problem is convexified in this article by devising `approximated' security strategies for both players that are based on approximated optimal game value. However, `approximated' strategies require full monitoring. Therefore, a simplistic yet effective `expected' strategy is also constructed for the LTE network that does not require full monitoring. The simulation results show that the smart jammer plays non-revealing and misleading strategies.

cs.GT↗

arXiv2019

Herdability of Linear Systems Based on Sign Patterns and Graph Structures

We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on herdability of a continuous time, linear time invariant system are presented. These show that the herdability of a linear system can be determined based on certain matrices, such as the controllability matrix, which arise in the study of controllability of linear systems. Second, the relationship between the sign pattern of the underlying graph structure of a system and the herdability properties of the system is investigated. In doing so the notion of sign herdability is introduced which captures classes of systems whose sign pattern determines their herdability. We identify a set of conditions, first on the sign pattern of the controllability matrix and then on the underlying graph structure, that ensure that the system is sign herdable.

eess.SY↗

arXiv2018

Infrastructure-free Localization of Aerial Robots with Ultrawideband Sensors

Robots in a swarm take advantage of a motion capture system or GPS sensors to obtain their global position. However, motion capture systems are environment-dependent and GPS sensors are not reliable in occluded environments. For a reliable and versatile operation in a swarm, robots must sense each other and interact locally. Motivated by this requirement, here we propose an on-board localization framework for multi-robot systems. Our framework consists of an anchor robot with three ultrawideband (UWB) sensors and a tag robot with a single UWB sensor. The anchor robot utilizes the three UWB sensors as a localization infrastructure and estimates the tag robot's location by using its on-board sensing and computational capabilities solely, without explicit inter-robot communication. We utilize a dual Monte-Carlo localization approach to capture the agile maneuvers of the tag robot with an acceptable precision. We validate the effectiveness of our algorithm with simulations and indoor and outdoor experiments on a two-drone setup. The proposed dual MCL algorithm yields highly accurate estimates for various speed profiles of the tag robot and demonstrates a superior performance over the standard particle filter and the extended Kalman Filter.

cs.RO↗

arXiv2018

Herding Positive, Complex Networks

The problem of controlling complex networks is of interest to disciplines ranging from biology to swarm robotics. However, controllability can be too strict a condition, failing to capture a range of desirable behaviors. Herdability, which describes the ability to drive a system to a specific set in the state space, was recently introduced as an alternative network control notion. This paper considers the application of herdability to the study of complex networks under the assumption that a positive system evolves on the network. The herdability of a class of networked systems is investigated and two problems related to ensuring system herdability are explored. The first is the input addition problem, which investigates which nodes in a network should receive inputs to ensure that the system is herdable. The second is a related problem of selecting the best single node from which to herd the network, in the case that a single node is guaranteed to make the system is herdable. In order to select the best herding node, a novel control energy based herdability centrality measure is introduced.

eess.SY↗

arXiv2018

Herdable Systems Over Signed, Directed Graphs

This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.

eess.SY↗

arXiv2018

Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with different update rules but same steady-state behavior. We present the framework in the context of two learning dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through an example setup of sensor coverage game that for each of these dynamics, the paths to stochastically stable states exhibit distinctive behaviors. Therefore, we propose multiple criteria to analyze and quantify the differences in the short and medium run behavior of stochastic learning dynamics. We derive and compare upper bounds on the expected hitting time to the set of Nash equilibria for both LLL and ML. For the medium to long-run behavior, we identify a set of tools from the theory of perturbed Markov chains that result in a hierarchical decomposition of the state space into collections of states called cycles. We compare LLL and ML based on the proposed criteria and develop invaluable insights into the comparative behavior of the two dynamics.

cs.LG↗

arXiv2018

Passivity and Evolutionary Game Dynamics

This paper investigates an energy conservation and dissipation -- passivity -- aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise systematic methods to examine passivity and to identify properties of passive dynamic models. Based on the methods, we describe how passivity is connected to stability in population games and illustrate stability of passive dynamic models using numerical simulations.

math.OC↗

arXiv2017

Efficient Strategy Computation in Zero-Sum Asymmetric Repeated Games

Zero-sum asymmetric games model decision making scenarios involving two competing players who have different information about the game being played. A particular case is that of nested information, where one (informed) player has superior information over the other (uninformed) player. This paper considers the case of nested information in repeated zero-sum games and studies the computation of strategies for both the informed and uninformed players for finite-horizon and discounted infinite-horizon nested information games. For finite-horizon settings, we exploit that for both players, the security strategy, and also the opponent's corresponding best response depend only on the informed player's history of actions. Using this property, we refine the sequence form, and formulate an LP computation of player strategies that is linear in the size of the uninformed player's action set. For the infinite-horizon discounted game, we construct LP formulations to compute the approximated security strategies for both players, and provide a bound on the performance difference between the approximated security strategies and the security strategies. Finally, we illustrate the results on a network interdiction game between an informed system administrator and uniformed intruder.

cs.GT↗

arXiv2017

Security Strategies of Both Players in Asymmetric Information Zero-Sum Stochastic Games with an Informed Controller

This paper considers a zero-sum two-player asymmetric information stochastic game where only one player knows the system state, and the transition law is controlled by the informed player only. For the informed player, it has been shown that the security strategy only depends on the belief and the current stage. We provide LP formulations whose size is only linear in the size of the uninformed player's action set to compute both history based and belief based security strategies. For the uninformed player, we focus on the regret, the difference between 0 and the future payoff guaranteed by the uninformed player in every possible state. Regret is a real vector of the same size as the belief, and depends only on the action of the informed player and the strategy of the uninformed player. This paper shows that the uninformed player has a security strategy that only depends on the regret and the current stage. LP formulations are then given to compute the history based security strategy, the regret at every stage, and the regret based security strategy. The size of the LP formulations are again linear in the size of the uninformed player action set. Finally, an intrusion detection problem is studied to demonstrate the main results in this paper.

cs.GT↗

arXiv2017

Global Games with Noisy Information Sharing

Global games form a subclass of games with incomplete information where a set of agents decide actions against a regime with an underlying fundamental $θ$ representing its power. Each agent has access to an independent noisy observation of $θ$. In order to capture the behavior of agents in a social network of information exchange we assume that agents share their observation in a noisy environment prior to making their decision. We show that global games with noisy sharing of information do not admit an intuitive type of threshold policy which only depends on agents' belief about the underlying $θ$. This is in contrast to the existing results on the threshold policy for the conventional set-up of global games. Motivated by this result, we investigate the existence of equilibrium strategies in a more general collection of threshold-type policies and show that such equilibrium strategies exist and are unique if the sharing of information happens over a sufficiently noisy environment.

cs.SI↗

arXiv2016

Energy Aware Architecture for Coordinated Mobility: An Approximate Dynamic Programming Approach

Our goal is to design distributed coordination strategies that enable agents to achieve global performance guarantees while minimizing the energy cost of their actions with an emphasis on feasibility for real-time implementation. As a motivating scenario that illustrates the importance of introducing energy awareness at the agent level, we consider a team of mobile nodes that are assigned the task of establishing a communication link between two base stations with minimum energy consumption. We formulate this problem as a dynamic program in which the total cost of each agent is the sum of both mobility and communication costs. To ensure that the solution is distributed and real time implementable, we propose multiple suboptimal policies based on the concepts of approximate dynamic programming. To provide performance guarantees, we compute upper bounds on the performance gap between the proposed suboptimal policies and the global optimal policy. Finally, we discuss merits and demerits of the proposed policies and compare their performance using simulations.

math.OC↗

arXiv2016

Networked SIS Epidemics with Awareness

We study an SIS epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe the epidemic is currently prevalent. A node's awareness is weighted by the fraction of infected neighbors in their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time Markov chains, from which mean-field approximations (MFA) are derived. The states of the MFA are interpreted as the nodes' probabilities of being infected. We show a sufficient condition for existence of a "metastable", or endemic, state of the awareness model coincides with that of the benchmark model. Furthermore, we use a coupling technique to give a full stochastic comparison analysis between the two chains, which serves as a probabilistic analogue to the MFA analysis. In particular, we show that adding awareness reduces the expectation of any epidemic metric on the space of sample paths, e.g. eradication time or total infections. We characterize the reduction in expectations in terms of the coupling distribution. In simulations, we evaluate the effect social distancing has on contact networks from different random graph families (geometric, Erdős-Renyi, and scale-free random networks).

cs.SI↗

arXiv2016

BLMA: A Blind Matching Algorithm with Application to Cognitive Radio Networks

We consider a two-sided matching problem with a defined notion of pairwise stability. We propose a distributed blind matching algorithm (BLMA) to solve the problem. We prove the solution produced by BLMA will converge to an $ε$-pairwise stable outcome with probability one. We then consider a matching problem in cognitive radio networks. Secondary users (SUs) are allowed access time to the spectrum belonging to the primary users (PUs) provided that they relay primary messages. We propose a realization of the BLMA to produce an $ε$-pairwise stable solution assuming quasi-convex and quasi-concave utilities. In the case of more general utility forms, we show another BLMA realization to provide a stable solution. Furthermore, we propose negotiation mechanism to bias the algorithm towards one side of the market. We use this mechanism to protect the exclusive rights of the PUs to the spectrum. In all such implementations of the BLMA, we impose a limited information exchange in the network so that agents can only calculate their own utilities, but no information is available about the utilities of any other users in the network.

cs.GT↗

arXiv2016

Disease dynamics on a network game: a little empathy goes a long way

Individuals change their behavior during an epidemic in response to whether they and/or those they interact with are healthy or sick. Healthy individuals are concerned about contracting a disease from their sick contacts and may utilize protective measures. Sick individuals may be concerned with spreading the disease to their healthy contacts and adopt preemptive measures. Yet, in practice both protective and preemptive changes in behavior come with costs. This paper proposes a stochastic network disease game model that captures the self-interests of individuals during the spread of a susceptible-infected-susceptible (SIS) disease where individuals react to current risk of disease spread, and their reactions together with the current state of the disease stochastically determine the next stage of the disease. We show that there is a critical level of concern, i.e., empathy, by the sick individuals above which disease is eradicated fast. Furthermore, we find that if the network and disease parameters are above the epidemic threshold, the risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals. This imbalance in the role played by the response of the infected versus the susceptible individuals in disease eradication affords critical policy insights.

cs.SI↗

arXiv2015

Learning Efficient Correlated Equilibria

The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.

cs.GT↗

arXiv2015

A Game-theoretic Formulation of the Homogeneous Self-Reconfiguration Problem

In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.

cs.MA↗

arXiv2015

Communication-Free Distributed Coverage for Networked Systems

In this paper, we present a communication-free algorithm for distributed coverage of an arbitrary network by a group of mobile agents with local sensing capabilities. The network is represented as a graph, and the agents are arbitrarily deployed on some nodes of the graph. Any node of the graph is covered if it is within the sensing range of at least one agent. The agents are mobile devices that aim to explore the graph and to optimize their locations in a decentralized fashion by relying only on their sensory inputs. We formulate this problem in a game theoretic setting and propose a communication-free learning algorithm for maximizing the coverage.

eess.SY↗

arXiv2015

Formation of Robust Multi-Agent Networks Through Self-Organizing Random Regular Graphs

Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m in [k, k + 2]. Accordingly, the agents improve the robustness of the network with a minimal change in the overall sparsity by optimizing the graph connectivity through the proposed local operations.

cs.MA↗