/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Federated learning involves training statistical models over remote devices or siloed data centers, such as mobile phones or hospitals, while keeping data localized. Training in heterogeneous and potentially massive networks introduces novel challenges that require a fundamental departure from standard approaches for large-scale machine learning, distributed optimization, and privacy-preserving data analysis. In this article, we discuss the unique characteristics and challenges of federated learning, provide a broad overview of current approaches, and outline several directions of future work that are relevant to a wide range of research communities.

Federated Learning: Challenges, Methods, and Future Directions

Federated Learning is a distributed machine learning approach which enables model training on a large corpus of decentralized data. We have built a scalable production system for Federated Learning in the domain of mobile devices, based on TensorFlow. In this paper, we describe the resulting high-level design, sketch some of the challenges and their solutions, and touch upon the open problems and future directions.

Towards Federated Learning at Scale: System Design

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

Advances and Open Problems in Federated Learning

A communication infrastructure is an essential part to the success of the emerging smart grid. A scalable and pervasive communication infrastructure is crucial in both construction and operation of a smart grid. In this paper, we present the background and motivation of communication infrastructures in smart grid systems. We also summarize major requirements that smart grid communications must meet. From the experience of several industrial trials on smart grid with communication infrastructures, we expect that the traditional carbon fuel based power plants can cooperate with emerging distributed renewable energy such as wind, solar, etc, to reduce the carbon fuel consumption and consequent green house gas such as carbon dioxide emission. The consumers can minimize their expense on energy by adjusting their intelligent home appliance operations to avoid the peak hours and utilize the renewable energy instead. We further explore the challenges for a communication infrastructure as the part of a complex smart grid system. Since a smart grid system might have over millions of consumers and devices, the demand of its reliability and security is extremely critical. Through a communication infrastructure, a smart grid can improve power reliability and quality to eliminate electricity blackout. Security is a challenging issue since the on-going smart grid systems facing increasing vulnerabilities as more and more automation, remote monitoring/controlling and supervision entities are interconnected.

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1315&context=electricalengineeringfacpub

A Survey on Smart Grid CommunicationInfrastructures: Motivations, Requirements andChallenges

Recently, there has been growing interest in solving consensus optimization problems in a multiagent network. In this paper, we develop a decentralized algorithm for the consensus optimization problem $\mathrm{minimize}_{x\in\mathbb{R}^p}~\bar{f}(x)=\frac{1}{n}\sum_{i=1}^n f_i(x),$ which is defined over a connected network of $n$ agents, where each function $f_i$ is held privately by agent $i$ and encodes the agent's data and objective. All the agents shall collaboratively find the minimizer while each agent can only communicate with its neighbors. Such a computation scheme avoids a data fusion center or long-distance communication and offers better load balance to the network. This paper proposes a novel decentralized exact first-order algorithm (abbreviated as EXTRA) to solve the consensus optimization problem. “Exact” means that it can converge to the exact solution. EXTRA uses a fixed, large step size, which can be determined independently of the network size or topology. The local variable of every a...

EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization

In decentralized consensus optimization, a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable, where their information exchange is restricted between the neighbors. To this end, one can first obtain a problem reformulation and then apply the alternating direction method of multipliers (ADMM). The method applies iterative computation at the individual agents and information exchange between the neighbors. This approach has been observed to converge quickly and deemed powerful. This paper establishes its linear convergence rate for the decentralized consensus optimization problem with strongly convex local objective functions. The theoretical convergence rate is explicitly given in terms of the network topology, the properties of local objective functions, and the algorithm parameter. This result is not only a performance guarantee but also a guideline toward accelerating the ADMM convergence.

On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient method and a gradient tracking technique. The DIGing algorithm uses doubly stochastic mixing matrices and employs fixed step-sizes and, yet, drives all the agents' iterates to a global and consensual minimizer. When the graphs are directed, in which case the implementation of doubly stochastic mixing matrices is unrealistic, we construct an algorithm that incorporates the push-sum protocol into the DIGing structure, thus obtaining the Push-DIGing algorithm. Push-DIGing uses column stochastic matrices and fixed step-sizes, but it still converges to a global and consensual minimizer. Under the strong convexity assumption, we prove that the algorithms converge at R-linear (geometric) rates as long as the step-sizes do not exceed some upper bounds. We establish explicit est...

Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs

Recently, there have been growing interests in solving consensus optimization problems in a multi-agent network. In this paper, we develop a decentralized algorithm for the consensus optimization problem $$\min\limits_{x\in\mathbb{R}^p}~\bar{f}(x)=\frac{1}{n}\sum\limits_{i=1}^n f_i(x),$$ which is defined over a connected network of $n$ agents, where each function $f_i$ is held privately by agent $i$ and encodes the agent's data and objective. All the agents shall collaboratively find the minimizer while each agent can only communicate with its neighbors. Such a computation scheme avoids a data fusion center or long-distance communication and offers better load balance to the network. 
This paper proposes a novel decentralized EXact firsT-ordeR Algorithm (abbreviated as EXTRA) to solve the consensus optimization problem. "exact" means that it can converge to the exact solution. EXTRA can use a fixed large step size, {which is independent of the network size}, and has synchronized iterations. The local variable of every agent $i$ converges uniformly and consensually to an exact minimizer of $\bar{f}$. In contrast, the well-known decentralized gradient descent (DGD) method must use diminishing step sizes in order to converge to an exact minimizer. EXTRA and DGD have the same choice of mixing matrices and similar per-iteration complexity. EXTRA, however, uses the gradients of last two iterates, unlike DGD which uses just that of last iterate. 
EXTRA has the best known convergence rates among the existing first-order decentralized algorithms. Specifically, if $f_i$'s are convex and have Lipschitz continuous gradients, EXTRA has an ergodic convergence rate $O(\frac{1}{k})$ in terms of the first-order optimality residual. If $\bar{f}$ is also restricted strongly convex, EXTRA converges to an optimal solution at a linear rate $O(C^{-k})$ for some constant $C>1$.

Wei Shi

Papers

EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization

On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs

EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization

Federated learning of predictive models from federated Electronic Health Records.