A distributed methodology for approximate uniform global minimum sharing

The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication network. We propose an adjustable approximate solution which enjoys several properties of crucial importance in applications. In particular, the proposed solution has good decentralization properties and it is scalable in that the number of local variables does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial conditions) asymptotic stability result is provided towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence can be recovered at the price of losing uniformity with respect to the initial time

Fast, Distributed Optimization Strategies for Resource Allocation in Networks

Many challenges in network science and engineering today arise from systems composed of many individual agents interacting over a network. Such problems range from humans interacting with each other in social networks to computers processing and exchanging information over wired or wireless networks. In any application where information is spread out spatially, solutions must address information aggregation in addition to the decision process itself. Intelligently addressing the trade off between information aggregation and decision accuracy is fundamental to finding solutions quickly and accurately. Network optimization challenges such as these have generated a lot of interest in distributed optimization methods. The field of distributed optimization deals with iterative methods which perform calculations using locally available information. Early methods such as subgradient descent suffer very slow convergence rates because the underlying optimization method is a first order method. My work addresses problems in the area of network optimization and control with an emphasis on accelerating the rate of convergence by using a faster underlying optimization method. In the case of convex network flow optimization, the problem is transformed to the dual domain, moving the equality constraints which guarantee flow conservation into the objective. The Newton direction can be computed locally by using a consensus iteration to solve a Poisson equation, but this requires a lot of communication between neighboring nodes. Accelerated Dual Descent (ADD) is an approximate Newton method, which significantly reduces the communication requirement. Defining a stochastic version of the convex network flow problem with edge capacities yields a problem equivalent to the queue stability problem studied in the backpressure literature. Accelerated Backpressure (ABP) is developed to solve the queue stabilization problem. A queue reduction method is introduced by merging ideas from integral control and momentum based optimization

Learning optimal control policies from data: a partially model-based actor-only approach

This dissertation presents new algorithms for learning optimal feed-back controllers directly from experimental data, considering the plant to be controlled as a black-box source of streaming input and output data. The presented methods fall in the Reinforcement Learning “actor-only” family of algorithms, employing a represen-tation (policy parameterization) of the controller as a function of the feedback values and of a set of parameters to be tuned. The optimization of a policy parameterization corresponds to the search of the set of parameters associated with the best value of a chosen performance index. Such a search is carried on via numerical opti-mization techniques, such as the Stochastic Gradient Descent algo-rithm and related techniques. The proposed methods are based on a combination of the data-driven policy search framework with some elements of the model-based scenario, in order to mitigate some of the drawbacks presented by the purely data-driven approach, while retaining a low modeling effort, as compared to the typical identif-cation and model-based control design scenario. In particular, we initially introduce an algorithm for the search of smooth control policies, considering both the online scenario (when new data are collected from the plant during the iterative policy syn-thesis, while the plant is also under closed-loop control) and the of-fine one (i.e. from open-loop data that were previously collected from the plant). The proposed method is then extended to learn non-smooth control policies, in particular hybrid control laws, op-timizing both the local controllers and the switching law directly from data. The described methods are then extended in order to be employed in a collaborative learning setup, considering multi-agent systems characterized by heavy similarities, exploiting a cloud-aided scenario to enhance the learning process by sharing information

Distributed Control Approaches for Power Systems

The energy industry is undergoing through a reconstruction from a monopolistic electricity market to a more open and transactive one. The next ­generation grid is a level playing field in terms of electricity transactions, where all customers have an equal opportunity. The emerging concepts of electricity prosumers are expected to have a significant impact on the retail electricity market. As a result, there is an urgent need to control the interactions among numerous consumers and pro­sumers. The existing control approaches can be divided into three categories, namely, centralized control, decentralized control, and distributed control. The majority of existing literature focuses on the centralized control. In most cases, the dedicated communication links are required to ex­change data between the central controller and the local agents. The centralized control approaches are suitable for relatively small­-scale systems without reconstructing the existing communication and control networks. However, as the number of consumers and prosumers are increasing to hun­dreds of thousands, there are some technical barriers on the centralized control-­based economic operations such as heavy computation burden and single point of failure. The decentralized control is an intermediate solution to address the above mentioned challenges. The overall objective is to maximize the benefits of local agents and there is no guarantee that the decisions made by each local agents can contribute to the global optimal decision of the entire system. The distributed control has the potential to solve the economic operation problems of multiple consumers and prosumers. Lo­cal agents can share information through two-­way communication links in order to find the global optimal decision. Application of distributed control methods in power system increase system’s scalability, alleviate monopoly and monopsony, improve the privacy and distribute computational load among various entities.Ph.D.College of Engineering & Computer ScienceUniversity of Michigan-Dearbornhttps://deepblue.lib.umich.edu/bitstream/2027.42/151932/1/Hajir Pourbabak Final Dissertation.pdfDescription of Hajir Pourbabak Final Dissertation.pdf : Dissertatio

Consensus Maximization: Theoretical Analysis and New Algorithms

The core of many computer vision systems is model fitting, which estimates a particular mathematical model given a set of input data. Due to the imperfection of the sensors, pre-processing steps and/or model assumptions, computer vision data usually contains outliers, which are abnormally distributed data points that can heavily reduce the accuracy of conventional model fitting methods. Robust fitting aims to make model fitting insensitive to outliers. Consensus maximization is one of the most popular paradigms for robust fitting, which is the main research subject of this thesis. Mathematically, consensus maximization is an optimization problem. To understand the theoretical hardness of this problem, a thorough analysis about its computational complexity is first conducted. Motivated by the theoretical analysis, novel techniques that improve different types of algorithms are then introduced. On one hand, an efficient and deterministic optimization approach is proposed. Unlike previous deterministic approaches, the proposed one does not rely on the relaxation of the original optimization problem. This property makes it much more effective at refining an initial solution. On the other hand, several techniques are proposed to significantly accelerate consensus maximization tree search. Tree search is one of the most efficient global optimization approaches for consensus maximization. Hence, the proposed techniques greatly improve the practicality of globally optimal consensus maximization algorithms. Finally, a consensus-maximization-based method is proposed to register terrestrial LiDAR point clouds. It demonstrates how to surpass the general theoretical hardness by using special problem structure (the rotation axis returned by the sensors), which simplify the problem and lead to application-oriented algorithms that are both efficient and globally optimal.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 202