Newton-ADMM: A Distributed GPU-Accelerated Optimizer for Multiclass Classification Problems

Fang, Chih-Hao; Kylasa, Sudhir B.; Roosta, Fred; Mahoney, Michael W.; Grama, Ananth

doi:10.1109/sc41405.2020.00061

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Xu et al (2017) [57] proposed consensus ADMM in which each agent automatically tuned the local penalty parameters in an adaptive manner. Fang et al (2020) [58] proposed a consensus ADMM approach whereby the Newton method was applied for each subproblem to improve the quality of the subproblem solutions. They [62] presented a randomized incremental primal dual method to solve the CO problem, whereby the dual variable over the connected multi-agent network in each iteration was only updated at a randomly selected node.…”

Section: Alternating Direction Methods Of Multipliersmentioning

confidence: 99%

Consensus Distributionally Robust Optimization With Phi-Divergence

Ohmori

2021

IEEE Access

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We study an efficient algorithm to solve the distributionally robust optimization (DRO) problem, which has recently attracted attention as a new paradigm for decision making in uncertain situations. In traditional stochastic programming, a decision is sought that minimizes the expected cost over uncertain parameters, given the probability distribution of the unknown parameters. In contrast, in DRO, robust decision making can be derived from data without assuming a probability distribution; thus, it is expected to provide a powerful method for data-driven decision making. However, solutions to DRO problems are computationally challenging and cannot be used for large-scale problems. Therefore, we propose a distributed optimization algorithm for DRO using consensus optimization (CO). CO is a decomposition method for large-scale problems and it is rapid because it decomposes the problem into smaller subproblems to solve. As different subproblems lead to different decisions, a coherence constraint is imposed to ensure agreement, thereby guaranteeing global convergence. We applied the proposed method to linear programming, quadratic programming, and second-order cone programming in numerical experiments and verified its effectiveness.

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Section: Alternating Direction Methods Of Multipliersmentioning

confidence: 99%

Consensus Distributionally Robust Optimization With Phi-Divergence

Ohmori

2021

IEEE Access

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“…The above objective function can be minimized using first-order optimization methods or second-order methods [54,55].…”

Section: Low-dimensional Embeddings Of Datasetmentioning

confidence: 99%

Identifying and analyzing sepsis states: A retrospective study on patients with sepsis in ICUs

Fang

Ravindra²,

Akhter³

et al. 2022

PLOS Digit Health

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Sepsis accounts for more than 50% of hospital deaths, and the associated cost ranks the highest among hospital admissions in the US. Improved understanding of disease states, progression, severity, and clinical markers has the potential to significantly improve patient outcomes and reduce cost. We develop a computational framework that identifies disease states in sepsis and models disease progression using clinical variables and samples in the MIMIC-III database. We identify six distinct patient states in sepsis, each associated with different manifestations of organ dysfunction. We find that patients in different sepsis states are statistically significantly composed of distinct populations with disparate demographic and comorbidity profiles. Our progression model accurately characterizes the severity level of each pathological trajectory and identifies significant changes in clinical variables and treatment actions during sepsis state transitions. Collectively, our framework provides a holistic view of sepsis, and our findings provide the basis for future development of clinical trials, prevention, and therapeutic strategies for sepsis.

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“…In recent years, a number of papers have proposed parallelizable variants of numerical optimization methods such as the interior point method, 37 parallel quadratic programming, 38 ADMM 39‐41 and other proximal algorithms 42,43 . In these approaches, GPUs are used to parallelize the involved algebraic operations and the solution of linear systems: the primal‐dual optimality conditions in interior point algorithms and equality‐constrained QPs in ADMM.…”

Section: Introductionmentioning

confidence: 99%

Massively parallelizable proximal algorithms for large‐scale stochastic optimal control problems

Sampathirao,

Patrinos,

Bemporad

et al. 2023

Optim Control Appl Methods

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Scenario‐based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First‐order methods are suitable as they can deal with such large‐scale problems, but may perform poorly and fail to converge within a reasonable number of iterations. To achieve a fast rate of convergence and high solution speeds, in this article, we propose the use of two proximal quasi‐Newtonian limited‐memory algorithms—minfbe applied to the dual problem and the Newton‐type alternating minimization algorithm (nama)—which can be massively parallelized on lockstep hardware such as graphics processing units. In particular, we use minfbe and nama to solve scenario‐based stochastic optimal control problems with affine dynamics, convex quadratic cost functions (with the stage cost functions being strongly convex in the control variable) and joint state‐input convex constraints. We demonstrate the performance of these methods, in terms of convergence speed and parallelizability, on large‐scale problems involving millions of variables.

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Newton-ADMM: A Distributed GPU-Accelerated Optimizer for Multiclass Classification Problems

Cited by 4 publications

References 15 publications

Consensus Distributionally Robust Optimization With Phi-Divergence

Consensus Distributionally Robust Optimization With Phi-Divergence

Identifying and analyzing sepsis states: A retrospective study on patients with sepsis in ICUs

Massively parallelizable proximal algorithms for large‐scale stochastic optimal control problems

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