Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss 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. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

We present Resilient Distributed Datasets (RDDs), a distributed memory abstraction that lets programmers perform in-memory computations on large clusters in a fault-tolerant manner. RDDs are motivated by two types of applications that current computing frameworks handle inefficiently: iterative algorithms and interactive data mining tools. In both cases, keeping data in memory can improve performance by an order of magnitude. To achieve fault tolerance efficiently, RDDs provide a restricted form of shared memory, based on coarse-grained transformations rather than fine-grained updates to shared state. However, we show that RDDs are expressive enough to capture a wide class of computations, including recent specialized programming models for iterative jobs, such as Pregel, and new applications that these models do not capture. We have implemented RDDs in a system called Spark, which we evaluate through a variety of user applications and benchmarks.

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Resilient distributed datasets: a fault-tolerant abstraction for in-memory cluster computing

In this paper, we review the background and state-of-the-art of big data. We first introduce the general background of big data and review related technologies, such as could computing, Internet of Things, data centers, and Hadoop. We then focus on the four phases of the value chain of big data, i.e., data generation, data acquisition, data storage, and data analysis. For each phase, we introduce the general background, discuss the technical challenges, and review the latest advances. We finally examine the several representative applications of big data, including enterprise management, Internet of Things, online social networks, medial applications, collective intelligence, and smart grid. These discussions aim to provide a comprehensive overview and big-picture to readers of this exciting area. This survey is concluded with a discussion of open problems and future directions.

Big Data: A Survey

The initial design of Apache Hadoop [1] was tightly focused on running massive, MapReduce jobs to process a web crawl. For increasingly diverse companies, Hadoop has become the data and computational agora---the de facto place where data and computational resources are shared and accessed. This broad adoption and ubiquitous usage has stretched the initial design well beyond its intended target, exposing two key shortcomings: 1) tight coupling of a specific programming model with the resource management infrastructure, forcing developers to abuse the MapReduce programming model, and 2) centralized handling of jobs' control flow, which resulted in endless scalability concerns for the scheduler. In this paper, we summarize the design, development, and current state of deployment of the next generation of Hadoop's compute platform: YARN. The new architecture we introduced decouples the programming model from the resource management infrastructure, and delegates many scheduling functions (e.g., task fault-tolerance) to per-application components. We provide experimental evidence demonstrating the improvements we made, confirm improved efficiency by reporting the experience of running YARN on production environments (including 100% of Yahoo! grids), and confirm the flexibility claims by discussing the porting of several programming frameworks onto YARN viz. Dryad, Giraph, Hoya, Hadoop MapReduce, REEF, Spark, Storm, Tez.

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Apache Hadoop YARN: yet another resource negotiator

The popularity of the Web and Internet commerce provides many extremely large datasets from which information can be gleaned by data mining. This book focuses on practical algorithms that have been used to solve key problems in data mining and which can be used on even the largest datasets. It begins with a discussion of the map-reduce framework, an important tool for parallelizing algorithms automatically. The authors explain the tricks of locality-sensitive hashing and stream processing algorithms for mining data that arrives too fast for exhaustive processing. The PageRank idea and related tricks for organizing the Web are covered next. Other chapters cover the problems of finding frequent itemsets and clustering. The final chapters cover two applications: recommendation systems and Web advertising, each vital in e-commerce. Written by two authorities in database and Web technologies, this book is essential reading for students and practitioners alike.

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Mining of Massive Datasets

A large-scale data processing system and method including a plurality of processes, wherein a master process assigns input data blocks to respective map processes and partitions of intermediate data are assigned to respective reduce processes. In each of the plurality of map processes an application-independent map program retrieves a sequence of input data blocks assigned thereto by the master process and applies an application-specific map function to each input data block in the sequence to produce the intermediate data and stores the intermediate data in high speed memory of the interconnected processors. Each of the plurality of reduce processes receives a respective partition of the intermediate data from the high speed memory of the interconnected processors while the map processes continue to process input data blocks an application-specific reduce function is applied to the respective partition of the intermediate data to produce output values.

System and method for limiting the impact of stragglers in large-scale parallel data processing

This paper introduces a parallel scheduling problem where a directed acyclic graph modeling t tasks and their dependencies needs to be executed on n unreliable workers. Worker i executes task j correctly with probability pi,j. The goal is to find a regimen E, that dictates how workers get assigned to tasks (possibly in parallel and redundantly) throughout execution, so as to minimize expected completion time. This fundamental parallel scheduling problem arises in grid computing and project management fields, and has several practical applications.We show a polynomial time algorithm for the problem restricted to the case when dag width is at most a constant and the number of workers is also at most a constant. These two restrictions may appear to be too severe. However, they are fundamentally required. Specifically, we demonstrate that the problem is NP-hard with constant number of workers when dag width can grow, and is also NP-hard with constant dag width when the number of workers can grow. When both dag width and the number of workers are unconstrained, then the problem is inapproximable within factor less than 5/4, unless P=NP.

Parallel scheduling of complex dags under uncertainty

The dissertation studies how distributed devices that are disconnected for long and unknown periods can efficiently perform a set of tasks. Given n distributed devices that must perform t independent tasks, known to each device, the goal is to schedule work of the devices locally, in the absence of communication, so that when communication is established between some devices at some later point of time, the devices that connect have performed few tasks redundantly beyond necessity. The dissertation gives a lower bound on redundant work, and randomized and deterministic schedules, that allow devices to avoid doing redundant work provably well. The lower bound shows how the wasted work increases as the devices progress in their work. When each disconnected device randomly selects its next task, from among the tasks remaining to be done, then the amount of work duplicated by any devices that reconnect, is close to the lower bound in a precise sense. In order to derandomize the construction of schedules, techniques from design theory, linear algebra, and graph theory are used. The topics developed within the dissertation are related to the theory of latin squares and coding theory. For example the lower bound shown in the dissertation generalizes the Second Johnson Bound. The dissertation also studies scheduling problems for shared memory systems. It shows a method for creating near-optimal instances of an algorithm of Anderson and Woll. The dissertation also shows a work-optimal deterministic algorithm for the asynchronous Certified Write-All problem.

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Distributed scheduling for disconnected cooperation

Earlier work has developed the underpinnings of the IC-scheduling theory, a framework for scheduling computations having intertask dependencies - modeled via directed acyclic graphs (DAGs) - for Internet-based computing. The goal of the schedules produced is to render tasks eligible for execution at the maximum possible rate, with the dual aim of 1) utilizing remote clients' computational resources well by always having work to allocate to an available client and 2) lessening the likelihood of a computation's stalling for lack of eligible tasks. The DAGs handled by the theory thus far are those that can be decomposed into a given collection of bipartite building block DAGs via the operation of DAG decomposition. A basic tool in constructing schedules is a relation >, which allows one to "prioritize" the scheduling of a complex DAG's building blocks. The current paper extends the IC-scheduling theory in two ways: by expanding significantly the repertoire of DAGs that the theory can schedule optimally and by allowing one sometimes to shortcut the algorithmic process required to find optimal schedules. The expanded repertoire now allows the theory to schedule optimally, among other DAGs, a large range of DAGs that are either "expansive", in the sense that they grow outward from their sources, or "reductive", in the sense that they grow inward toward their sinks. The algorithmic shortcuts allow one to "read off" an optimal schedule for a DAG from a given optimal schedule for the DAG's dual, which is obtained by reversing all arcs (thereby exchanging the roles of sources and sinks).

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Advances in IC-Scheduling Theory: Scheduling Expansive and Reductive Dags and Scheduling Dags via Duality

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. Despite the ubiquity of large graphs and their commercial importance, we know of no scalable general-purpose system for implementing graph algorithms in a distributed environment. To address distributed processing of real-life graphs, we defined a model of computation and realized it through a scalable and fault-tolerant system called Pregel, with an expressive and flexible API. The high-level organization of Pregel programs is inspired by Valiant’s Bulk Synchronous Parallel model. Pregel computations consist of a sequence of iterations, called superstep s. During a superstep the framework invokes a userdefined Compute() function for each vertex, conceptually in parallel. The function specifies behavior at a single vertex v and a single superstep S. It can read messages sent to v in superstep S − 1, send messages to other vertices that will be received at superstep S + 1, and modify the state of v and its outgoing edges. Messages are typically sent along outgoing edges, but a message may be sent to any vertex whose identifier is known. A program terminates when all vertices declare that they are done. The input and output are both directed graphs. They are often but not always isomorphic, because vertices and edges can be added and removed during computation. Userdefined handlers are applied to resolve conflicts for concurrent mutations. The vertex-centric flavor of programming in Pregel is similar to the MapReduce model in that programmers focus on a local action, processing a single item at a time, which the system then lifts to computation on a large dataset. The synchronicity of the Pregel model simplifies writing correct programs and simplifies reasoning about the inter-

Grzegorz Malewicz

Papers

System and method for limiting the impact of stragglers in large-scale parallel data processing

Parallel scheduling of complex dags under uncertainty

Distributed scheduling for disconnected cooperation

Advances in IC-Scheduling Theory: Scheduling Expansive and Reductive Dags and Scheduling Dags via Duality

Pregel: a system for large-scale graph processing - "ABSTRACT"