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Recent Advances in Randomized Method...

Liu, Jie.

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Recent Advances in Randomized Methods for Big Data Optimization.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Recent Advances in Randomized Methods for Big Data Optimization./
Author:	Liu, Jie.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	187 p.
Notes:	Source: Dissertation Abstracts International, Volume: 80-07(E), Section: B.
Contained By:	Dissertation Abstracts International80-07B(E).
Subject:	Artificial intelligence. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10973840
ISBN:	9780438888036

Recent Advances in Randomized Methods for Big Data Optimization.
Liu, Jie.

Recent Advances in Randomized Methods for Big Data Optimization. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 187 p.

Source: Dissertation Abstracts International, Volume: 80-07(E), Section: B.

Thesis (Ph.D.)--Lehigh University, 2018.

In this thesis, we discuss and develop randomized algorithms for big data problems. In particular, we study the finite-sum optimization with newly emerged variance-reduction optimization methods (Chapter 2), explore the efficiency of second-order information applied to both convex and non-convex finite-sum objectives (Chapter 3) and employ the fast first-order method in power system problems (Chapter 4).

ISBN: 9780438888036Subjects--Topical Terms:

516317
Artificial intelligence.

Recent Advances in Randomized Methods for Big Data Optimization.
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245 1 0 $a Recent Advances in Randomized Methods for Big Data Optimization.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 187 p.
500 $a Source: Dissertation Abstracts International, Volume: 80-07(E), Section: B.
500 $a Adviser: Martin Takac.
502 $a Thesis (Ph.D.)--Lehigh University, 2018.
520 $a In this thesis, we discuss and develop randomized algorithms for big data problems. In particular, we study the finite-sum optimization with newly emerged variance-reduction optimization methods (Chapter 2), explore the efficiency of second-order information applied to both convex and non-convex finite-sum objectives (Chapter 3) and employ the fast first-order method in power system problems (Chapter 4).
520 $a In Chapter 2, we propose two variance-reduced gradient algorithms---mS2GD and SARAH. mS2GD incorporates a mini-batching scheme for improving the theoretical complexity and practical performance of SVRG/S2GD, aiming to minimize a strongly convex function represented as the sum of an average of a large number of smooth convex functions and a simple non-smooth convex regularizer. While SARAH, short for StochAstic Recursive grAdient algoritHm and using a stochastic recursive gradient, targets at minimizing the average of a large number of smooth functions for both convex and non-convex cases. Both methods fall into the category of variance-reduction optimization, and obtain a total complexity of O((n + kappa)log(1/epsilon)) to achieve an epsilon-accuracy solution for strongly convex objectives, while SARAH also maintains a sub-linear convergence for non-convex problems. Meanwhile, SARAH has a practical variant SARAH+ due to its linear convergence of the expected stochastic gradients in inner loops.
520 $a In Chapter 3, we declare that randomized batches can be applied with second-order information, as to improve upon convergence in both theory and practice, with a framework of L-BFGS as a novel approach to finite-sum optimization problems. We provide theoretical analyses for both convex and non-convex objectives. Meanwhile, we propose LBFGS-F as a variant where Fisher information matrix is used instead of Hessian information, and prove it applicable to a distributed environment within the popular applications of least-square and cross-entropy losses.
520 $a In Chapter 4, we develop fast randomized algorithms for solving polynomial optimization problems on the applications of alternating-current optimal power flows (ACOPF) in power system field. The traditional research on power system problem focuses on solvers using second-order method, while no randomized algorithms have been developed. First, we propose a coordinate-descent algorithm as an online solver, applied for solving time-varying optimization problems in power systems. We bound the difference between the current approximate optimal cost generated by our algorithm and the optimal cost for a relaxation using the most recent data from above by a function of the properties of the instance and the rate of change to the instance over time. Second, we focus on a steady-state problem in power systems, and study means of switching from solving a convex relaxation to Newton method working on a non-convex (augmented) Lagrangian of the problem.
590 $a School code: 0105.
650 4 $a Artificial intelligence. $3 516317
650 4 $a Statistics. $3 517247
650 4 $a Industrial engineering. $3 526216
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710 2 $a Lehigh University. $b Information and Systems Engineering. $3 3175565
773 0 $t Dissertation Abstracts International $g 80-07B(E).
790 $a 0105
791 $a Ph.D.
792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10973840