Optimal Stochastic And Distributed Algorithms For Machine Learning

Stochastic and data-distributed optimization algorithms have received lots of attention from the machine learning community due to the tremendous demand from the large-scale learning and the big-data related optimization. A lot of stochastic and deterministic learning algorithms are proposed recently under various application scenarios. Nevertheless, many of these algorithms are based on heuristics and their optimality in terms of the generalization error is not sufficiently justified. In this talk, I will explain the concept of an optimal learning algorithm, and show that given a time budget and proper hypothesis space, only those achieving the lower bounds of the estimation error and the optimization error are optimal. Guided by this concept, we investigated the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We proposed a novel algorithm named Accelerated Nonsmooth Stochastic Gradient Descent, which exploits the structure of common nonsmooth loss functions to achieve optimal convergence rates for a class of problems including SVMs. It is the first stochastic algorithm that can achieve the optimal O(1/t) rate for minimizing nonsmooth loss functions. The fast rates are confirmed by empirical comparisons with state-of-the-art algorithms including the averaged SGD. The Alternating Direction Method of Multipliers (ADMM) is another flexible method to explore function structures. In the second part we proposed stochastic ADMM that can be applied to a general class of convex and nonsmooth functions, beyond the smooth and separable least squares loss used in lasso. We also demonstrate the rates of convergence for our algorithm under various structural assumptions of the stochastic function: O(1/sqrt{t}) for convex functions and O(log t/t) for strongly convex functions. A novel application named Graph-Guided SVM is proposed to demonstrate the usefulness of our algorithm. We also extend the scalability of stochastic algorithms to nonlinear kernel machines, where the problem is formulated as a constrained dual quadratic optimization. The simplex constraint can be handled by the classic Frank-Wolfe method. The proposed stochastic Frank-Wolfe methods achieve comparable or even better accuracies than state-of-the-art batch and online kernel SVM solvers, and are significantly faster. The last part investigates the problem of data-distributed learning. We formulate it as a consensus-constrained optimization problem and solve it with ADMM. It turns out that the underlying communication topology is a key factor in achieving a balance between a fast learning rate and computation resource consumption. We analyze the linear convergence behavior of consensus ADMM so as to characterize the interplay between the communication topology and the penalty parameters used in ADMM. We observe that given optimal parameters, the complete bipartite and the master-slave graphs exhibit the fastest convergence, followed by bi-regular graphs.

This book presents the state of the art in distributed machine learning algorithms that are based on gradient optimization methods. In the big data era, large-scale datasets pose enormous challenges for the existing machine learning systems. As such, implementing machine learning algorithms in a distributed environment has become a key technology, and recent research has shown gradient-based iterative optimization to be an effective solution. Focusing on methods that can speed up large-scale gradient optimization through both algorithm optimizations and careful system implementations, the book introduces three essential techniques in designing a gradient optimization algorithm to train a distributed machine learning model: parallel strategy, data compression and synchronization protocol. Written in a tutorial style, it covers a range of topics, from fundamental knowledge to a number of carefully designed algorithms and systems of distributed machine learning. It will appeal to a broad audience in the field of machine learning, artificial intelligence, big data and database management.

This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

This book discusses state-of-the-art stochastic optimization algorithms for distributed machine learning and analyzes their convergence speed. The book first introduces stochastic gradient descent (SGD) and its distributed version, synchronous SGD, where the task of computing gradients is divided across several worker nodes. The author discusses several algorithms that improve the scalability and communication efficiency of synchronous SGD, such as asynchronous SGD, local-update SGD, quantized and sparsified SGD, and decentralized SGD. For each of these algorithms, the book analyzes its error versus iterations convergence, and the runtime spent per iteration. The author shows that each of these strategies to reduce communication or synchronization delays encounters a fundamental trade-off between error and runtime.

Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

This book focuses on improving the performance (convergence rate, communication efficiency, computational efficiency, etc.) of algorithms in the context of distributed optimization in networked systems and their successful application to real-world applications (smart grids and online learning). Readers may be particularly interested in the sections on consensus protocols, optimization skills, accelerated mechanisms, event-triggered strategies, variance-reduction communication techniques, etc., in connection with distributed optimization in various networked systems. This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike.

META-HEURISTIC ALGORITHMS FOR ADVANCED DISTRIBUTED SYSTEMS Discover a collection of meta-heuristic algorithms for distributed systems in different application domains Meta-heuristic techniques are increasingly gaining favor as tools for optimizing distributed systems—generally, to enhance the utility and precision of database searches. Carefully applied, they can increase system effectiveness, streamline operations, and reduce cost. Since many of these techniques are derived from nature, they offer considerable scope for research and development, with the result that this field is growing rapidly. Meta-Heuristic Algorithms for Advanced Distributed Systems offers an overview of these techniques and their applications in various distributed systems. With strategies based on both global and local searching, it covers a wide range of key topics related to meta-heuristic algorithms. Those interested in the latest developments in distributed systems will find this book indispensable. Meta-Heuristic Algorithms for Advanced Distributed Systems readers will also find: Analysis of security issues, distributed system design, stochastic optimization techniques, and more Detailed discussion of meta-heuristic techniques such as the genetic algorithm, particle swam optimization, and many others Applications of optimized distribution systems in healthcare and other key??industries Meta-Heuristic Algorithms for Advanced Distributed Systems is ideal for academics and researchers studying distributed systems, their design, and their applications.

This book constitutes the refereed proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2001, held in Berlin, Germany in December 2001. The nine revised full papers presented together with four invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to the design and analysis, experimental evaluation, and real-world application of stochasitc algorithms; in particular, new algorithmic ideas involving stochastic decisions and exploiting probabilistic properties of the underlying problem are introduced. Among the application fields are network and distributed algorithms, local search methods, and computational learning.

This book provides the fundamental theory of distributed optimization, game and learning. It includes those working directly in optimization,-and also many other issues like time-varying topology, communication delay, equality or inequality constraints,-and random projections. This book is meant for the researcher and engineer who uses distributed optimization, game and learning theory in fields like dynamic economic dispatch, demand response management and PHEV routing of smart grids.

Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.