Distributed Optimization with Application to Power Systems and Control

Mathematical optimization techniques are among the most successful tools for controlling technical systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization overcome this limitation. Classical approaches, however, are often not applicable due to non-convexities. This work develops one of the first frameworks for distributed non-convex optimization

Distributed Optimization with Application to Power Systems and Control

In many engineering domains, systems are composed of partially independent subsystems—power systems are composed of distribution and transmission systems, teams of robots are composed of individual robots, and chemical process systems are composed of vessels, heat exchangers and reactors. Often, these subsystems should reach a common goal such as satisfying a power demand with minimum cost, flying in a formation, or reaching an optimal set-point. At the same time, limited information exchange is desirable—for confidentiality reasons but also due to communication constraints. Moreover, a fast and reliable decision process is key as applications might be safety-critical. Mathematical optimization techniques are among the most successful tools for controlling systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization control the subsystems in a distributed or decentralized fashion, reducing or avoiding central coordination. These methods have a long and successful history. Classical distributed optimization algorithms, however, are typically designed for convex problems. Hence, they are only partially applicable in the above domains since many of them lead to optimization problems with non-convex constraints. This thesis develops one of the first frameworks for distributed and decentralized optimization with non-convex constraints. Based on the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, a bi-level distributed ALADIN framework is presented, solving the coordination step of ALADIN in a decentralized fashion. This framework can handle various decentralized inner algorithms, two of which we develop here: a decentralized variant of the Alternating Direction Method of Multipliers (ADMM) and a novel decentralized Conjugate Gradient algorithm. Decentralized conjugate gradient is to the best of our knowledge the first decentralized algorithm with a guarantee of convergence to the exact solution in a finite number of iterates. Sufficient conditions for fast local convergence of bi-level ALADIN are derived. Bi-level ALADIN strongly reduces the communication and coordination effort of ALADIN and preserves its fast convergence guarantees. We illustrate these properties on challenging problems from power systems and control, and compare performance to the widely used ADMM. The developed methods are implemented in the open-source MATLAB toolbox ALADIN-—one of the first toolboxes for decentralized non-convex optimization. ALADIN- comes with a rich set of application examples from different domains showing its broad applicability. As an additional contribution, this thesis provides new insights why state-of-the-art distributed algorithms might encounter issues for constrained problems

Distributed Optimization with Application to Power Systems and Control

Mathematical optimization techniques are among the most successful tools for controlling technical systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization overcome this limitation. Classical approaches, however, are often not applicable due to non-convexities. This work develops one of the first frameworks for distributed non-convex optimization

Efficient Methods for Distributed Machine Learning and Resource Management in the Internet-of-Things

University of Minnesota Ph.D. dissertation.June 2019. Major: Electrical/Computer Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); x, 190 pages.Undoubtedly, this century evolves in a world of interconnected entities, where the notion of Internet-of-Things (IoT) plays a central role in the proliferation of linked devices and objects. In this context, the present dissertation deals with large-scale networked systems including IoT that consist of heterogeneous components, and can operate in unknown environments. The focus is on the theoretical and algorithmic issues at the intersection of optimization, machine learning, and networked systems. Specifically, the research objectives and innovative claims include: (T1) Scalable distributed machine learning approaches for efficient IoT implementation; and, (T2) Enhanced resource management policies for IoT by leveraging machine learning advances. Conventional machine learning approaches require centralizing the users' data on one machine or in a data center. Considering the massive amount of IoT devices, centralized learning becomes computationally intractable, and rises serious privacy concerns. The widespread consensus today is that besides data centers at the cloud, future machine learning tasks have to be performed starting from the network edge, namely mobile devices. The first contribution offers innovative distributed learning methods tailored for heterogeneous IoT setups, and with reduced communication overhead. The resultant distributed algorithm can afford provably reduced communication complexity in distributed machine learning. From learning to control, reinforcement learning will play a critical role in many complex IoT tasks such as autonomous vehicles. In this context, the thesis introduces a distributed reinforcement learning approach featured with its high communication efficiency. Optimally allocating computing and communication resources is a crucial task in IoT. The second novelty pertains to learning-aided optimization tools tailored for resource management tasks. To date, most resource management schemes are based on a pure optimization viewpoint (e.g., the dual (sub)gradient method), which incurs suboptimal performance. From the vantage point of IoT, the idea is to leverage the abundant historical data collected by devices, and formulate the resource management problem as an empirical risk minimization task --- a central topic in machine learning research. By cross-fertilizing advances of optimization and learning theory, a learn-and-adapt resource management framework is developed. An upshot of the second part is its ability to account for the feedback-limited nature of tasks in IoT. Typically, solving resource allocation problems necessitates knowledge of the models that map a resource variable to its cost or utility. Targeting scenarios where models are not available, a model-free learning scheme is developed in this thesis, along with its bandit version. These algorithms come with provable performance guarantees, even when knowledge about the underlying systems is obtained only through repeated interactions with the environment. The overarching objective of this dissertation is to wed state-of-the-art optimization and machine learning tools with the emerging IoT paradigm, in a way that they can inspire and reinforce the development of each other, with the ultimate goal of benefiting daily life