arXiv subjects

Sindri Magnusson

Publications and source records attributed to Sindri Magnusson.

14 recordsLinked to original sources

arXiv2024

Asynchronous Distributed Optimization with Delay-free Parameters

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or use fixed step-sizes that depend on and decrease with an upper bound of the delays. Not only are such delay bounds hard to obtain in advance, but they also tend to be large and rarely attained, resulting in unnecessarily slow convergence. This paper develops asynchronous versions of two distributed algorithms, Prox-DGD and DGD-ATC, for solving consensus optimization problems over undirected networks. In contrast to alternatives, our algorithms can converge to the fixed point set of their synchronous counterparts using step-sizes that are independent of the delays. We establish convergence guarantees for convex and strongly convex problems under both partial and total asynchrony. We also show that the convergence speed of the two asynchronous methods adjusts to the actual level of asynchrony rather than being constrained by the worst-case. Numerical experiments demonstrate a strong practical performance of our asynchronous algorithms.

math.OC↗

arXiv2023

Delay-agnostic Asynchronous Distributed Optimization

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to obtain in advance, but it is also large and therefore results in unnecessarily slow convergence. This paper develops asynchronous versions of two distributed algorithms, DGD and DGD-ATC, for solving consensus optimization problems over undirected networks. In contrast to alternatives, our algorithms can converge to the fixed-point set of their synchronous counterparts using step-sizes that are independent of the delays. We establish convergence guarantees under both partial and total asynchrony. The practical performance of our algorithms is demonstrated by numerical experiments.

math.OC↗

arXiv2023

Delay-agnostic Asynchronous Coordinate Update Algorithm

We propose a delay-agnostic asynchronous coordinate update algorithm (DEGAS) for computing operator fixed points, with applications to asynchronous optimization. DEGAS includes novel asynchronous variants of ADMM and block-coordinate descent as special cases. We prove that DEGAS converges under both bounded and unbounded delays under delay-free parameter conditions. We also validate by theory and experiments that DEGAS adapts well to the actual delays. The effectiveness of DEGAS is demonstrated by numerical experiments on classification problems.

math.OC↗

arXiv2022

Federated Learning for IoUT: Concepts, Applications, Challenges and Opportunities

Internet of Underwater Things (IoUT) have gained rapid momentum over the past decade with applications spanning from environmental monitoring and exploration, defence applications, etc. The traditional IoUT systems use machine learning (ML) approaches which cater the needs of reliability, efficiency and timeliness. However, an extensive review of the various studies conducted highlight the significance of data privacy and security in IoUT frameworks as a predominant factor in achieving desired outcomes in mission critical applications. Federated learning (FL) is a secured, decentralized framework which is a recent development in machine learning, that will help in fulfilling the challenges faced by conventional ML approaches in IoUT. This paper presents an overview of the various applications of FL in IoUT, its challenges, open issues and indicates direction of future research prospects.

cs.LG↗

arXiv2022

Distributed Safe Resource Allocation using Barrier Functions

Resource allocation plays a central role in many networked systems such as smart grids, communication networks and urban transportation systems. In these systems, many constraints have physical meaning and having feasible allocation is often vital to avoid system breakdown. Hence, algorithms with asymptotic feasibility guarantees are often insufficient since it is impractical to run algorithms for an infinite number of rounds. This paper proposes a distributed feasible method (DFM) for safe resource allocation based on barrier functions. In DFM, every iterate is feasible and thus safe to implement. We prove that under mild conditions, DFM converges to an arbitrarily small neighbourhood of the optimal solution. Numerical experiments demonstrate the competitive performance of DFM.

math.OC↗

arXiv2022

Delay-adaptive step-sizes for asynchronous learning

In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information delays in the system to determine learning rates. Not only are such bounds hard to obtain in advance, but they also result in unnecessarily slow convergence. In this paper, we show that it is possible to use learning rates that depend on the actual time-varying delays in the system. We develop general convergence results for delay-adaptive asynchronous iterations and specialize these to proximal incremental gradient descent and block-coordinate descent algorithms. For each of these methods, we demonstrate how delays can be measured on-line, present delay-adaptive step-size policies, and illustrate their theoretical and practical advantages over the state-of-the-art.

cs.LG↗

arXiv2022

Leakage Localization in Water Distribution Networks: A Model-Based Approach

The paper studies the problem of leakage localization in water distribution networks. For the case of a single pipe that suffers from a single leak, by taking recourse to pressure and flow measurements, and assuming those are noiseless, we provide a closed-form expression for leak localization, leak exponent and leak constant. For the aforementioned setting, but with noisy pressure and flow measurements, an expression for estimating the location of the leak is provided. Finally, assuming the existence of a single leak, for a network comprising of more than one pipe and assuming that the network has a tree structure, we provide a systematic procedure for determining the leak location, the leak exponent, and the leak constant

eess.SY↗

arXiv2022

Optimal convergence rates of totally asynchronous optimization

Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive explicit convergence rates for the proximal incremental aggregated gradient (PIAG) and the asynchronous block-coordinate descent (Async-BCD) methods under a specific model of total asynchrony, and show that the derived rates are order-optimal. The convergence bounds provide an insightful understanding of how the growth rate of the delays deteriorates the convergence times of the algorithms. Our theoretical findings are demonstrated by a numerical example.

math.OC↗

arXiv2021

A New Family of Feasible Methods for Distributed Resource Allocation

Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic feasibility guarantees for the iterates, since overallocation of resources easily causes systems to break down. In this paper, we develop a distributed resource reallocation algorithm where every iteration produces a feasible allocation. The algorithm is fully distributed in the sense that nodes communicate only with neighbors over a given communication network. We prove that under mild conditions the algorithm converges to a point arbitrarily close to the optimal resource allocation. Numerical experiments demonstrate the competitive practical performance of the algorithm.

math.OC↗

arXiv2020

Communication-efficient Variance-reduced Stochastic Gradient Descent

We consider the problem of communication efficient distributed optimization where multiple nodes exchange important algorithm information in every iteration to solve large problems. In particular, we focus on the stochastic variance-reduced gradient and propose a novel approach to make it communication-efficient. That is, we compress the communicated information to a few bits while preserving the linear convergence rate of the original uncompressed algorithm. Comprehensive theoretical and numerical analyses on real datasets reveal that our algorithm can significantly reduce the communication complexity, by as much as 95\%, with almost no noticeable penalty. Moreover, it is much more robust to quantization (in terms of maintaining the true minimizer and the convergence rate) than the state-of-the-art algorithms for solving distributed optimization problems. Our results have important implications for using machine learning over internet-of-things and mobile networks.

cs.LG↗

arXiv2019

Voltage Control Using Limited Communication

In electricity distribution networks, the increasing penetration of renewable energy generation necessitates faster and more sophisticated voltage controls. Unfortunately, recent research shows that local voltage control fails in achieving the desired regulation, unless there is communication between the controllers. However, the communication infrastructure for distribution systems is less reliable and less ubiquitous as compared to that for the bulk transmission system. In this paper, we design distributed voltage control that uses limited communication. That is, only neighboring buses need to communicate a few bits between each other for each control step. We investigate how these controllers can achieve the desired asymptotic behavior of the voltage regulation and we provide upper bounds on the number of bits that are needed to ensure a predefined accuracy of the regulation. Finally, we illustrate the results by numerical simulations.

math.OC↗

arXiv2017

Convergence of Limited Communications Gradient Methods

Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to communication limitations posed by the real-world infrastructures. This work investigates fundamental properties of distributed optimization based on gradient methods, where gradient information is communicated using limited number of bits. In particular, a general class of quantized gradient methods are studied where the gradient direction is approximated by a finite quantization set. Sufficient and necessary conditions are provided on such a quantization set to guarantee that the methods minimize any convex objective function with Lipschitz continuous gradient and a nonempty and bounded set of optimizers. A lower bound on the cardinality of the quantization set is provided, along with specific examples of minimal quantizations. Convergence rate results are established that connect the fineness of the quantization and the number of iterations needed to reach a predefined solution accuracy. Generalizations of the results to a relevant class of constrained problems using projections are considered. Finally, the results are illustrated by simulations of practical systems.

math.OC↗

arXiv2016

Distributed Resource Allocation Using One-Way Communication with Applications to Power Networks

Typical coordination schemes for future power grids require two-way communications. Since the number of end power-consuming devices is large, the bandwidth requirements for such two-way communication schemes may be prohibitive. Motivated by this observation, we study distributed coordination schemes that require only one-way limited communications. In particular, we investigate how dual descent distributed optimization algorithm can be employed in power networks using one-way communication. In this iterative algorithm, system coordinators broadcast coordinating (or pricing) signals to the users/devices who update power consumption based on the received signal. Then system coordinators update the coordinating signals based on the physical measurement of the aggregate power usage. We provide conditions to guarantee the feasibility of the aggregated power usage at each iteration so as to avoid blackout. Furthermore, we prove the convergence of algorithms under these conditions, and establish its rate of convergence. We illustrate the performance of our algorithms using numerical simulations. These results show that one-way limited communication may be viable for coordinating/operating the future smart grids.

eess.SY↗

arXiv2016

Robustness Analysis for an Online Decentralized Descent Power allocation algorithm

As independent service providers shift from conventional energy to renewable energy sources, the power distribution system will likely experience increasingly significant fluctuation in supply, given the uncertain and intermittent nature of renewable sources like wind and solar energy. These fluctuations in power generation, coupled with time-varying consumer demands of electricity and the massive scale of power distribution networks present the need to not only design real-time decentralized power allocation algorithms, but also characterize how effective they are given fast-changing consumer demands and power generation capacities. In this paper, we present an Online Decentralized Dual Descent (OD3) power allocation algorithm and determine (in the worst case) how much of observed social welfare and price volatility can be explained by fluctuations in generation capacity and consumer demand. Convergence properties and performance guarantees of the OD3 algorithm are analyzed by characterizing the difference between the online decision and the optimal decision. The theoretical results in the paper are validated and illustrated by numerical experiments using real data.

eess.SY↗