arXiv subjects

Tansu Alpcan

Publications and source records attributed to Tansu Alpcan.

54 records · Page 3Linked to original sources

arXiv2017

Lower Bounds on the Complexity of Solving Two Classes of Non-cooperative Games

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with $ε$ accuracy. First, we consider the class $\mathcal{G}$ of all $N$-player non-cooperative games with a continuous action space that admit at least one NE. Using information-theoretic inequalities, we derive a lower bound on the complexity of solving $\mathcal{G}$ that depends on the Kolmogorov $2ε$-capacity of the constraint set and the total capacity of the communication channels. We also derive a lower bound on the complexity of solving games in $\mathcal{G}$ which depends on the volume and surface area of the constraint set. We next consider the class of all $N$-player non-cooperative games with at least one NE such that the players' utility functions satisfy a certain (differential) constraint. We derive lower bounds on the complexity of solving this game class under both Gaussian and non-Gaussian noise models. Our result in the non-Gaussian case is derived by establishing a connection between the Kullback-Leibler distance and Fisher information.

cs.IT↗

arXiv2016

Large-Scale Strategic Games and Adversarial Machine Learning

Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative) games where a finite number of individual players each have a large number of continuous decision variables and input data points. Such high-dimensional decision spaces and big data sets lead to computational challenges, relating to efforts in non-linear optimization scaling up to large systems of variables. In addition to these computational challenges, real-world players often have limited information about their preference parameters due to the prohibitive cost of identifying them or due to operating in dynamic online settings. The challenge of limited information is exacerbated in high dimensions and big data sets. Motivated by both computational and information limitations that constrain the direct solution of big strategic games, our investigation centers around reductions using linear transformations such as random projection methods and their effect on Nash equilibrium solutions. Specific analytical results are presented for quadratic games and approximations. In addition, an adversarial learning game is presented where random projection and sampling schemes are investigated.

cs.GT↗

arXiv2016

Dynamic Control of Interference Limited Underlay D2D Network

Device-to-Device (D2D) communication appears as a key communication paradigm to realizing the vision of Internet of Things (IoT) into reality by supporting heterogeneous objects interconnection in a large scale network. These devices may be many types of objects with embedded intelligence and communication capabilities, e.g., smart phones, cars, or home appliances. The issue in in this type of communication is the interference to cellular communication caused by D2D communication. Thus, proper power control and resource allocation should be coordinated in D2D network to prevent excessive interference and drastic decrease in the throughput of the cellular system. In this paper, we consider the problem of cross-layer resource allocation in time-varying cellular wireless networks with D2D communication and incorporate average interference to cellular system as a quality-of-service constraint. Specifically, each D2D pair in the network injects packets to its queue, at rates chosen in order to maximize a global utility function, subject to network stability and interference constraints. The interference constraint enforces an arbitrarily low interference to the cellular system caused by D2D communication. We first obtain the stability region for the multiuser systems assuming that the nodes have full channel state information (CSI) of their neighbors. Then, we provide a joint flow control and scheduling scheme, which is proven to achieve a utility arbitrarily close to the maximum achievable utility. Finally, we address the consequences of practical implementation issue such as distributed scheduling by a designing algorithm, which is capable of taking advantage of diversity gain introduced by fading channels. We demonstrate the efficacy of our policies by numerical studies under various network conditions.

cs.NI↗

arXiv2016

Convergence Analysis of Quantized Primal-dual Algorithm in Network Utility Maximization Problems

This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions under linear constraints. In the asymptotic scenario, we use the information theoretic notion of differential entropy power to establish universal lower bounds on the exponential convergence rates of joint primal dual, primal and dual variables under optimum achieving quantization schemes. These results provide trade offs between the speed of exponential convergence, the agents objective functions, the communication bit rates, and the number of agents and constraints. In the non-asymptotic scenario, we obtain lower bounds on the mean square distance of joint primal dual, primal and dual variables from the optimal solution for any finite time instance. These bounds hold regardless of the quantization scheme used.

math.OC↗

arXiv2016

Game-Theoretic Model of Incentivizing Privacy-Aware Users to Consent to Location Tracking

Nowadays, mobile users have a vast number of applications and services at their disposal. Each of these might impose some privacy threats on users' "Personally Identifiable Information" (PII). Location privacy is a crucial part of PII, and as such, privacy-aware users wish to maximize it. This privacy can be, for instance, threatened by a company, which collects users' traces and shares them with third parties. To maximize their location privacy, users can decide to get offline so that the company cannot localize their devices. The longer a user stays connected to a network, the more services he might receive, but his location privacy decreases. In this paper, we analyze the trade-off between location privacy, the level of services that a user experiences, and the profit of the company. To this end, we formulate a Stackelberg Bayesian game between the User (follower) and the Company (leader). We present theoretical results characterizing the equilibria of the game. To the best of our knowledge, our work is the first to model the economically rational decision-making of the service provider (i.e., the Company) in conjunction with the rational decision-making of users who wish to protect their location privacy. To evaluate the performance of our approach, we have used real-data from a testbed, and we have also shown that the game-theoretic strategy of the Company outperforms non-strategic methods. Finally, we have considered different User privacy types, and have determined the service level that incentivizes the User to stay connected as long as possible.

cs.GT↗

arXiv2012

Competition and Regulation in Wireless Services Markets

We consider a wireless services market where a set of operators compete for a large common pool of users. The latter have a reservation utility of U0 units or, equivalently, an alternative option to satisfy their communication needs. The operators must satisfy these minimum requirements in order to attract the users. We model the users decisions and interaction as an evolutionary game and the competition among the operators as a non cooperative price game which is proved to be a potential game. For each set of prices selected by the operators, the evolutionary game attains a different stationary point. We show that the outcome of both games depend on the reservation utility of the users and the amount of spectrum W the operators have at their disposal. We express the market welfare and the revenue of the operators as functions of these two parameters. Accordingly, we consider the scenario where a regulating agency is able to intervene and change the outcome of the market by tuning W and/or U0. Different regulators may have different objectives and criteria according to which they intervene. We analyze the various possible regulation methods and discuss their requirements, implications and impact on the market.

cs.NI↗

arXiv2012

Throughput Optimal Scheduling with Dynamic Channel Feedback

It is well known that opportunistic scheduling algorithms are throughput optimal under full knowledge of channel and network conditions. However, these algorithms achieve a hypothetical achievable rate region which does not take into account the overhead associated with channel probing and feedback required to obtain the full channel state information at every slot. We adopt a channel probing model where $β$ fraction of time slot is consumed for acquiring the channel state information (CSI) of a single channel. In this work, we design a joint scheduling and channel probing algorithm named SDF by considering the overhead of obtaining the channel state information. We first analytically prove SDF algorithm can support $1+ε$ fraction of of the full rate region achieved when all users are probed where $ε$ depends on the expected number of users which are not probed. Then, for homogenous channel, we show that when the number of users in the network is greater than 3, $ε> 0$, i.e., we guarantee to expand the rate region. In addition, for heterogenous channels, we prove the conditions under which SDF guarantees to increase the rate region. We also demonstrate numerically in a realistic simulation setting that this rate region can be achieved by probing only less than 50% of all channels in a CDMA based cellular network utilizing high data rate protocol under normal channel conditions.

cs.NI↗

arXiv2011

Incentive Mechanisms for Hierarchical Spectrum Markets

In this paper, we study spectrum allocation mechanisms in hierarchical multi-layer markets which are expected to proliferate in the near future based on the current spectrum policy reform proposals. We consider a setting where a state agency sells spectrum channels to Primary Operators (POs) who subsequently resell them to Secondary Operators (SOs) through auctions. We show that these hierarchical markets do not result in a socially efficient spectrum allocation which is aimed by the agency, due to lack of coordination among the entities in different layers and the inherently selfish revenue-maximizing strategy of POs. In order to reconcile these opposing objectives, we propose an incentive mechanism which aligns the strategy and the actions of the POs with the objective of the agency, and thus leads to system performance improvement in terms of social welfare. This pricing-based scheme constitutes a method for hierarchical market regulation. A basic component of the proposed incentive mechanism is a novel auction scheme which enables POs to allocate their spectrum by balancing their derived revenue and the welfare of the SOs.

cs.NI↗

arXiv2011

A Framework for Optimization under Limited Information

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points that are obtained over time through costly observations. This paper presents an optimization framework that takes into account the information collection (observation), estimation (regression), and optimization (maximization) aspects in a holistic and structured manner. Explicitly quantifying the information acquired at each optimization step using the entropy measure from information theory, the (nonconvex) objective function to be optimized (maximized) is modeled and estimated by adopting a Bayesian approach and using Gaussian processes as a state-of-the-art regression method. The resulting iterative scheme allows the decision maker to solve the problem by expressing preferences for each aspect quantitatively and concurrently.

math.OC↗

arXiv2011

Dual Control with Active Learning using Gaussian Process Regression

In many real world problems, control decisions have to be made with limited information. The controller may have no a priori (or even posteriori) data on the nonlinear system, except from a limited number of points that are obtained over time. This is either due to high cost of observation or the highly non-stationary nature of the system. The resulting conflict between information collection (identification, exploration) and control (optimization, exploitation) necessitates an active learning approach for iteratively selecting the control actions which concurrently provide the data points for system identification. This paper presents a dual control approach where the information acquired at each control step is quantified using the entropy measure from information theory and serves as the training input to a state-of-the-art Gaussian process regression (Bayesian learning) method. The explicit quantification of the information obtained from each data point allows for iterative optimization of both identification and control objectives. The approach developed is illustrated with two examples: control of logistic map as a chaotic system and position control of a cart with inverted pendulum.

math.OC↗

arXiv2010

Incentive Games and Mechanisms for Risk Management

Incentives play an important role in (security and IT) risk management of a large-scale organization with multiple autonomous divisions. This paper presents an incentive mechanism design framework for risk management based on a game-theoretic approach. The risk manager acts as a mechanism designer providing rules and incentive factors such as assistance or subsidies to divisions or units, which are modeled as selfish players of a strategic (noncooperative) game. Based on this model, incentive mechanisms with various objectives are developed that satisfy efficiency, preference-compatibility, and strategy-proofness criteria. In addition, iterative and distributed algorithms are presented, which can be implemented under information limitations such as the risk manager not knowing the individual units' preferences. An example scenario illustrates the framework and results numerically. The incentive mechanism design approach presented is useful for not only deriving guidelines but also developing computer-assistance systems for large-scale risk management.

cs.GT↗

arXiv2010

A Unified Mechanism Design Framework for Networked Systems

Mechanisms such as auctions and pricing schemes are utilized to design strategic (noncooperative) games for networked systems. Although the participating players are selfish, these mechanisms ensure that the game outcome is optimal with respect to a global criterion (e.g. maximizing a social welfare function), preference-compatible, and strategy-proof, i.e. players have no reason to deceive the designer. The mechanism designer achieves these objectives by introducing specific rules and incentives to the players; in this case by adding resource prices to their utilities. In auction-based mechanisms, the mechanism designer explicitly allocates the resources based on bids of the participants in addition to setting prices. Alternatively, pricing mechanisms enforce global objectives only by charging the players for the resources they have utilized. In either setting, the player preferences represented by utility functions may be coupled or decoupled, i.e. they depend on other player's actions or only on player's own actions, respectively. The unified framework and its information structures are illustrated through multiple example resource allocation problems from wireless and wired networks.

cs.GT↗

arXiv2010

An Optimization and Control Theoretic Approach to Noncooperative Game Design

This paper investigates design of noncooperative games from an optimization and control theoretic perspective. Pricing mechanisms are used as a design tool to ensure that the Nash equilibrium of a fairly general class of noncooperative games satisfies certain global objectives such as welfare maximization or achieving a certain level of quality-of-service (QoS). The class of games considered provide a theoretical basis for decentralized resource allocation and control problems including network congestion control, wireless uplink power control, and optical power control. The game design problem is analyzed under different knowledge assumptions (full versus limited information) and design objectives (QoS versus utility maximization) for separable and non-separable utility functions. The ``price of anarchy'' is shown not to be an inherent feature of full-information games that incorporate pricing mechanisms. Moreover, a simple linear pricing is shown to be sufficient for design of Nash equilibrium according to a chosen global objective for a fairly general class of games. Stability properties of the game and pricing dynamics are studied under the assumption of time-scale separation and in two separate time-scales. Thus, sufficient conditions are derived, which allow the designer to place the Nash equilibrium solution or to guide the system trajectory to a desired region or point. The obtained results are illustrated with a number of examples.

cs.GT↗

arXiv2010

Fictitious Play with Time-Invariant Frequency Update for Network Security

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process, where players do not have access to each other's payoff matrix. Each has to observe the other's actions up to present and plays the action generated based on the best response to these observations. In a regular fictitious play process, each player makes a maximum likelihood estimate of her opponent's mixed strategy, which results in a time-varying update based on the previous estimate and current action. In this paper, we explore an alternative scheme for frequency update, whose mean dynamic is instead time-invariant. We examine convergence properties of the mean dynamic of the fictitious play process with such an update scheme, and establish local stability of the equilibrium point when both players are restricted to two actions. We also propose an adaptive algorithm based on this time-invariant frequency update.

cs.GT↗

arXiv2010

Security Games with Decision and Observation Errors

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process. Players do not have access to each other's payoff matrix. Each has to observe the other's actions up to present and plays the action generated based on the best response to these observations. However, when the game is played over a communication network, there are several practical issues that need to be taken into account: First, the players may make random decision errors from time to time. Second, the players' observations of each other's previous actions may be incorrect. The players will try to compensate for these errors based on the information they have. We examine convergence property of the game in such scenarios, and establish convergence to the equilibrium point under some mild assumptions when both players are restricted to two actions.

cs.GT↗

arXiv2010

Stochastic Games for Security in Networks with Interdependent Nodes

This paper studies a stochastic game theoretic approach to security and intrusion detection in communication and computer networks. Specifically, an Attacker and a Defender take part in a two-player game over a network of nodes whose security assets and vulnerabilities are correlated. Such a network can be modeled using weighted directed graphs with the edges representing the influence among the nodes. The game can be formulated as a non-cooperative zero-sum or nonzero-sum stochastic game. However, due to correlation among the nodes, if some nodes are compromised, the effective security assets and vulnerabilities of the remaining ones will not stay the same in general, which leads to complex system dynamics. We examine existence, uniqueness, and structure of the solution and also provide numerical examples to illustrate our model.

cs.CR↗

arXiv2010

Distributed Rate Allocation Policies for Multi-Homed Video Streaming over Heterogeneous Access Networks

We consider the problem of rate allocation among multiple simultaneous video streams sharing multiple heterogeneous access networks. We develop and evaluate an analytical framework for optimal rate allocation based on observed available bit rate (ABR) and round-trip time (RTT) over each access network and video distortion-rate (DR) characteristics. The rate allocation is formulated as a convex optimization problem that minimizes the total expected distortion of all video streams. We present a distributed approximation of its solution and compare its performance against H-infinity optimal control and two heuristic schemes based on TCP-style additive-increase-multiplicative decrease (AIMD) principles. The various rate allocation schemes are evaluated in simulations of multiple high-definition (HD) video streams sharing multiple access networks. Our results demonstrate that, in comparison with heuristic AIMD-based schemes, both media-aware allocation and H-infinity optimal control benefit from proactive congestion avoidance and reduce the average packet loss rate from 45% to below 2%. Improvement in average received video quality ranges between 1.5 to 10.7 dB in PSNR for various background traffic loads and video playout deadlines. Media-aware allocation further exploits its knowledge of the video DR characteristics to achieve a more balanced video quality among all streams.

cs.MM↗

arXiv2009

A Robust Control Framework for Malware Filtering

We study and develop a robust control framework for malware filtering and network security. We investigate the malware filtering problem by capturing the tradeoff between increased security on one hand and continued usability of the network on the other. We analyze the problem using a linear control system model with a quadratic cost structure and develop algorithms based on H infinity-optimal control theory. A dynamic feedback filter is derived and shown via numerical analysis to be an improvement over various heuristic approaches to malware filtering. The results are verified and demonstrated with packet level simulations on the Ns-2 network simulator.

cs.CR↗