A Sharp Estimate on the Transient Time of Distributed Stochastic Gradient Descent.

This paper is concerned with minimizing the average of n cost functions over a network in which agents may communicate and exchange information with each other. We consider the setting where only noisy gradient information is available. To solve the problem, we study the distributed stochastic gradient descent (DSGD) method and perform a non-asymptotic convergence analysis. For strongly convex and smooth objective functions, in expectation, DSGD asymptotically achieves the optimal network independent convergence rate compared to centralized stochastic gradient descent (SGD). Our main contribution is to characterize the transient time needed for DSGD to approach the asymptotic convergence rate. Moreover, we construct a "hard" optimization problem that proves the sharpness of the obtained result. Numerical experiments demonstrate the tightness of the theoretical results.

Asymptotic Network Independence in Distributed Stochastic Optimization for Machine Learning.

We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property, which is achieved whenever a distributed method executed over a network of n nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network. We explain this property through an example involving the training of ML models and sketch a short mathematical analysis for comparing the performance of distributed stochastic gradient descent (DSGD) with centralized stochastic gradient decent (SGD).

Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions.

We consider the standard model of distributed optimization of a sum of functions F ( z ) = ∑ i = 1 n f i ( z ) , where node i in a network holds the function fi (z). We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node i is capable of generating gradients of its function fi (z) corrupted by zero-mean bounded-support additive noise at each step, (ii) F(z) is strongly convex, and (iii) each fi (z) has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions f 1(z), …, fn (z) at each step.

Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints.

Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic questions in the analysis of social opinion dynamics: (i) Will a belief system converge? (ii) How long does it take to converge? (iii) Where does it converge? We provide graph-theoretic answers to these questions for a model of opinion dynamics of a belief system with logic constraints. Our results make plain the implicit dependence of the convergence properties of a belief system on the underlying social network and on the set of logic constraints that relate beliefs on different statements. Moreover, we provide an explicit analysis of a variety of commonly used large-scale network models.

Federated learning of predictive models from federated Electronic Health Records.

BACKGROUND: In an era of "big data," computationally efficient and privacy-aware solutions for large-scale machine learning problems become crucial, especially in the healthcare domain, where large amounts of data are stored in different locations and owned by different entities. Past research has been focused on centralized algorithms, which assume the existence of a central data repository (database) which stores and can process the data from all participants. Such an architecture, however, can be impractical when data are not centrally located, it does not scale well to very large datasets, and introduces single-point of failure risks which could compromise the integrity and privacy of the data. Given scores of data widely spread across hospitals/individuals, a decentralized computationally scalable methodology is very much in need. OBJECTIVE: We aim at solving a binary supervised classification problem to predict hospitalizations for cardiac events using a distributed algorithm. We seek to develop a general decentralized optimization framework enabling multiple data holders to collaborate and converge to a common predictive model, without explicitly exchanging raw data. METHODS: We focus on the soft-margin l1-regularized sparse Support Vector Machine (sSVM) classifier. We develop an iterative cluster Primal Dual Splitting (cPDS) algorithm for solving the large-scale sSVM problem in a decentralized fashion. Such a distributed learning scheme is relevant for multi-institutional collaborations or peer-to-peer applications, allowing the data holders to collaborate, while keeping every participant's data private. RESULTS: We test cPDS on the problem of predicting hospitalizations due to heart diseases within a calendar year based on information in the patients Electronic Health Records prior to that year. cPDS converges faster than centralized methods at the cost of some communication between agents. It also converges faster and with less communication overhead compared to an alternative distributed algorithm. In both cases, it achieves similar prediction accuracy measured by the Area Under the Receiver Operating Characteristic Curve (AUC) of the classifier. We extract important features discovered by the algorithm that are predictive of future hospitalizations, thus providing a way to interpret the classification results and inform prevention efforts.