Electrical and Electronic Engineering - Research Publications
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ItemA framework for optimization under limited information(SPRINGER, 2013-03)
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ItemAn Information Analysis of Iterative Algorithms for Network Utility Maximization and Strategic Games(IEEE, 2019)A variety of resource allocation problems on networked systems, for example, those in cyber-physical systems or Internet-of-things applications, require distributed solution methods. Modern distributed algorithms usually require bandwidth-limited digital communication between the system and its users, who are often modeled as independent decision makers with individual preferences. This paper presents a quantitative information flow and knowledge gain analysis of decentralized iterative algorithms with bounded trajectories in the context of convex network utility maximization problems and strategic games with a unique Nash equilibrium solution. First, a novel generic framework is introduced to quantify knowledge gain in network resource allocation problems using entropy by taking into account priors in the solution space. Second, a general result is presented on the interplay between quantization of information and distributed algorithm performance both for linear and sublinear convergence. Third, information flow in distributed algorithms is studied and a lower bound is derived on the total amount of information exchanged for convergence under uniform quantization. The well-known primal-dual decomposition algorithm is used as an example to illustrate the results. Finally, convergence guarantees for distributed algorithms with estimation are investigated. This paper establishes specific links between information concepts and iterative algorithms in addition to building a foundation for integrating learning schemes into distributed optimization.
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ItemDetection of Anomalous Communications with SDRs and Unsupervised Adversarial Learning(IEEE, 2019-02-08)Software-defined radios (SDRs) with substantial cognitive (computing) and networking capabilities provide an opportunity for observing radio communications in an area and potentially identifying malicious rogue agents. Assuming a prevalence of encryption methods, a cognitive network of such SDRs can be used as a low-cost and flexible scanner/sensor array for distributed detection of anomalous communications by focusing on their statistical characteristics. Identifying rogue agents based on their wireless communications patterns is not a trivial task, especially when they deliberately try to mask their activities. We address this problem using a novel framework that utilizes adversarial learning, non-linear data transformations to minimize the rogue agent's attempts at masking their activities, and game theory to predict the behavior of rogue agents and take the necessary countermeasures.
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ItemA game-theoretic analysis of the adversarial boyd-kuramoto model(SpringerLink, 2018-01-01)The “Boyd” model, also known as the “OODA loop”, represents the cyclic decision processes of individuals and organisations in a variety of adversarial situations. Combined with the Kuramoto model, which provides a mathematical foundation for describing the behaviour of a set of coupled or networked oscillators, the Boyd-Kuramoto model captures strategic (cyclic) decision making in competitive environments. This paper presents a novel game-theoretic approach to the Boyd-Kuramoto dynamical model in complex and networked systems. A two-player, Red versus Blue, strategic (non-cooperative) game is defined to describe the competitive interactions and individual decision cycles of Red and Blue agent populations. We study the model analytically in the regime of near phase synchrony where linearisation approximations are possible. We find that we can solve for the Nash equilibrium of the game in closed form, and that it only depends on the parameters defining the fixed point of the dynamical system. A detailed numerical analysis of the finite version of the game investigates the behaviour of the underlying networked Kuramoto oscillators and yields a unique, dominant Nash equilibrium solution. The obtained Nash equilibrium is further studied analytically in a region where the underlying Boyd-Kuramoto dynamics are stable. The result suggests that only the fixed point of the dynamical system plays a role, consist with the analytical solution. Finally, the impact of other variations of the Boyd-Kuramoto parameters on the game outcomes are studied numerically, confirming the observations from fixed point approaches. It is observed that many parameters of the Kuramoto model affect the NE solution of the current game formulation much less than initially stipulated, arguably due to the time-scale separation between the underlying Kuramoto model and the static game formulation.
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ItemImpact of quantized inter-agent communications on game-theoretic and distributed optimization algorithms(Springer, 2018-01-01)Quantized inter-agent communications in game-theoretic and distributed optimization algorithms generate uncertainty that affects the asymptotic and transient behavior of such algorithms. This chapter uses the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of primal-dual and gradient-based Nash seeking algorithms under quantized communications. These bounds depend on the inter-agent data rate and the local behavior of the agents’ objective functions, and are independent of the quantizer structure. The presented 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. For the proposed Nash seeking algorithm, the transient performance is studied and an upper bound on the average time required to settle inside a specified ball around the Nash equilibrium is derived under uniform quantization. Furthermore, an upper bound on the probability that the agents’ actions lie outside this ball is established. This bound decays double exponentially with time.
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ItemInformation Constrained and Finite-Time Distributed Optimisation Algorithms(IEEE, 2017)This paper studies the delay-accuracy trade-off for an unconstrained quadratic Network Utility Maximization (NUM) problem, which is solved by a distributed, consensus based, constant step-size, gradient-descent algorithm. Information theoretic tools such as entropy power inequality are used to analyse the convergence rate of the algorithm under quantised inter-agent communication. A finite-time distributed algorithm is proposed to solve the problem under synchronised message passing. For a system with N agents, the algorithm reaches any desired accuracy within 2N iterations, by adjusting the step-size, α. However, if N is quite large or if the agents are constrained by their memory or computational capacities, asymptotic convergence algorithms are preferred to arrive within a permissible neighbourhood of the optimal solution. The analytical tools and algorithms developed shed light to delay-accuracy trade-off required for many real-time IoT applications, e.g., smart traffic control and smart grid. As an illustrative example, we use our algorithm to implement an intersection management application, where distributed computation and communication capabilities of smart vehicles and road side units increase the efficiency of an intersection.
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ItemLong-Term Stochastic Planning in Electricity Markets Under Carbon Cap Constraint: A Bayesian Game Approach(IEEE, 2016-01-01)Carbon price in an electricity market provides incentives for carbon emission abatement and renewable generation technologies. Policies constraining or penalizing carbon emissions can significantly impact the capacity planning decisions of both fossil-fueled and renewable generators. Uncertainties due to intermittency of various renewable generators can also affect the carbon emission policies. This paper proposes a Cournot-based long-term capacity expansion model taking into account carbon cap constraint for a partly concentrated electricity market dealing with stochastic renewables using a Bayesian game. The stochastic game is formulated as a centralized convex optimization problem and solved to obtain a Bayes-Nash Equilibrium (Bayes-NE) point. The stochastic nature of a generic electricity market is illustrated with a set of scenarios for wind availability, in which three generation firms (coal, gas, and wind) decide on their generation and long-term capacity investment strategies. Carbon price is derived as the dual variable of the carbon cap constraint. Embedding the carbon cap constraint in the game indicates more investment on renewable generators and less on fossil-fueled power plants. However, the higher level of intermittency from renewable generation leads to a higher carbon price to meet the cap constraint. This paves the way towards storage technologies and diversification of distributed generation as means to encounter intermittency in renewable generation.
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ItemInformation metrics for model selection in function estimation(IEEE, 2014-01-01)A model selection framework is presented for function estimation under limited information, where only a small set of (noisy) data points are available for inferring the nonconvex unknown function of interest. The framework introduces information-theoretic metrics which quantify model complexity and are used in a multi-objective formulation of the function estimation problem. The intricate relationship between information obtained through observations and model complexity is investigated. The framework is applied to the hyperparameter selection problem in Gaussian Process Regression. As a result of its generality, the framework introduced is applicable to a variety of settings and practical problems with information limitations such as channel estimation, black-box optimisation, and dual control.
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ItemCan we measure the difficulty of an optimization problem?(IEEE, 2014)Can we measure the difficulty of an optimization problem? Although optimization plays a crucial role in modern science and technology, a formal framework that puts problems and solution algorithms into a broader context has not been established. This paper presents a conceptual approach which gives a positive answer to the question for a broad class of optimization problems. Adopting an information and computational perspective, the proposed framework builds upon Shannon and algorithmic information theories. As a starting point, a concrete model and definition of optimization problems is provided. Then, a formal definition of optimization difficulty is introduced which builds upon algorithmic information theory. Following an initial analysis, lower and upper bounds on optimization difficulty are established. One of the upper-bounds is closely related to Shannon information theory and black-box optimization. Finally, various computational issues and future research directions are discussed.