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Register a new userAnalysis and Implementation of an Asynchronous Optimization Algorithm for the Parameter Server
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Added by
Arda Aytekin
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly non-smooth) regularizers and general convex constraints. When the empirical data loss is strongly convex, we establish linear convergence rate, give explicit expressions for step-size choices that guarantee convergence to the optimum, and bound the associated convergence factors. The expressions have an explicit dependence on the degree of asynchrony and recover classical results under synchronous operation. Simulations and implementations on commercial compute clouds validate our findings.
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Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous (due to different computational capabilities or different communication delays), synchronous and cyclic operations are inefficient since they will leave workers idle waiting for the slower nodes to complete their computations. In this paper, we propose an asynchronous mini-batch algorithm for regularized stochastic optimization problems with smooth loss functions that eliminates idle waiting and allows workers to run at their maximal update rates. We show that by suitably choosing the step-size values, the algorithm achieves a rate of the order $O(1/sqrt{T})$ for general convex regularization functions, and the rate $O(1/T)$ for strongly convex regularization functions, where $T$ is the number of iterations. In both cases, the impact of asynchrony on the convergence rate of our algorithm is asymptotically negligible, and a near-linear speedup in the number of workers can be expected. Theoretical results are confirmed in real implementations on a distributed computing infrastructure.
Optimization in distributed networks plays a central role in almost all distributed machine learning problems. In principle, the use of distributed task allocation has reduced the computational time, allowing better response rates and higher data reliability. However, for these computational algorithms to run effectively in complex distributed systems, the algorithms ought to compensate for communication asynchrony, network node failures and delays known as stragglers. These issues can change the effective connection topology of the network, which may vary over time, thus hindering the optimization process. In this paper, we propose a new distributed unconstrained optimization algorithm for minimizing a convex function which is adaptable to a parameter server network. In particular, the network worker nodes solve their local optimization problems, allowing the computation of their local coded gradients, which will be sent to different server nodes. Then within this parameter server platform each server node aggregates its communicated local gradients, allowing convergence to the desired optimizer. This algorithm is robust to network s worker node failures, disconnection, or delaying nodes known as stragglers. One way to overcome the straggler problem is to allow coding over the network. We further extend this coding framework to enhance the convergence of the proposed algorithm under such varying network topologies. By using coding and utilizing evaluations of gradients of uniformly bounded delay we further enhance the proposed algorithm performance. Finally, we implement the proposed scheme in MATLAB and provide comparative results demonstrating the effectiveness of the proposed framework
We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptions of previous models, and in some cases yield improved upper bounds on the convergence rates. We proceed to apply our framework to develop and analyze KroMagnon: a novel, parallel, sparse stochastic variance-reduced gradient (SVRG) algorithm. We demonstrate experimentally on a 16-core machine that the sparse and parallel version of SVRG is in some cases more than four orders of magnitude faster than the standard SVRG algorithm.
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require synchronization of all workers at each iteration, which is hard to scale and could result in the under-utilization of computation resources due to the heterogeneity of the subproblems. To address those limitations of synchronous schemes, this paper proposes an asynchronous distributed optimization method based on the Alternating Direction Method of Multipliers (ADMM) for non-convex optimization. The proposed method only requires local communications and allows each worker to perform local updates with information from a subset of but not all neighbors. We provide sufficient conditions on the problem formulation, the choice of algorithm parameter and network delay, and show that under those mild conditions, the proposed asynchronous ADMM method asymptotically converges to the KKT point of the non-convex problem. We validate the effectiveness of asynchronous ADMM by applying it to the Optimal Power Flow problem in multiple power systems and show that the convergence of the proposed asynchronous scheme could be faster than its synchronous counterpart in large-scale applications.
Algorithm NCL is designed for general smooth optimization problems where first and second derivatives are available, including problems whose constraints may not be linearly independent at a solution (i.e., do not satisfy the LICQ). It is equivalent to the LANCELOT augmented Lagrangian method, reformulated as a short sequence of nonlinearly constrained subproblems that can be solved efficiently by IPOPT and KNITRO, with warm starts on each subproblem. We give numerical results from a Julia implementation of Algorithm NCL on tax policy models that do not satisfy the LICQ, and on nonlinear least-squares problems and general problems from the CUTEst test set.
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