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Efficient Algorithms for Modern Mach...

Ding, Lisang,

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Efficient Algorithms for Modern Machine Learning Optimization /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Efficient Algorithms for Modern Machine Learning Optimization // Lisang Ding.
Author:	Ding, Lisang,
Description:	1 electronic resource (135 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Applied mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32045196
ISBN:	9798315793328

Efficient Algorithms for Modern Machine Learning Optimization /
Ding, Lisang,

Efficient Algorithms for Modern Machine Learning Optimization /Lisang Ding. - 1 electronic resource (135 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

The training of machine learning models is a central topic in modern computational research and is often formulated as an optimization problem. However, the optimization landscape in machine learning presents new and complex challenges. This dissertation addresses two related optimization problems: decentralized optimization, which arises in distributed training settings, and sum-of-minimum optimization, which emerges in mixed-model training.For the decentralized optimization problem, we revisit and construct a communication-optimal exact consensus scheme. This scheme is then judiciously integrated into the decentralized stochastic gradient descent algorithm. The proposed decentralized algorithm is scalable to any number of computing nodes and achieves state-of-the-art performance, which requires a transient iteration complexity of O(n3) and a communication overhead of one.For the sum-of-minimum optimization problem, we identify a novel connection to generalized clustering problems. Leveraging this insight, we develop a two-phase algorithm. In the initialization phase, we generalize the k-means++ clustering method; in the iteration phase, we apply a variant of the Lloyd algorithm. Theoretically, a tight initialization error bound and a convergence rate are provided.For both problems, extensive numerical experiments are provided to illustrate the empirical performance of the proposed algorithms.

English

ISBN: 9798315793328Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Machine learning

Efficient Algorithms for Modern Machine Learning Optimization /
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Osher, Stanley J.; Yin, Wotao Committee members: Ryu, Ernest K.; Montufar Cuartas, Guido Francisco; Schaeffer, Hayden Kyler.
502 $b Ph.D. $c University of California, Los Angeles $d 2025.
520 $a The training of machine learning models is a central topic in modern computational research and is often formulated as an optimization problem. However, the optimization landscape in machine learning presents new and complex challenges. This dissertation addresses two related optimization problems: decentralized optimization, which arises in distributed training settings, and sum-of-minimum optimization, which emerges in mixed-model training.For the decentralized optimization problem, we revisit and construct a communication-optimal exact consensus scheme. This scheme is then judiciously integrated into the decentralized stochastic gradient descent algorithm. The proposed decentralized algorithm is scalable to any number of computing nodes and achieves state-of-the-art performance, which requires a transient iteration complexity of O(n3) and a communication overhead of one.For the sum-of-minimum optimization problem, we identify a novel connection to generalized clustering problems. Leveraging this insight, we develop a two-phase algorithm. In the initialization phase, we generalize the k-means++ clustering method; in the iteration phase, we apply a variant of the Lloyd algorithm. Theoretically, a tight initialization error bound and a convergence rate are provided.For both problems, extensive numerical experiments are provided to illustrate the empirical performance of the proposed algorithms.
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590 $a School code: 0031
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
650 4 $a Computational physics. $3 3343998
653 $a Machine learning
653 $a Optimization problem
653 $a Lloyd algorithm
653 $a Stochastic gradient
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690 $a 0405
690 $a 0216
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $e degree granting institution. $3 3821487
720 1 $a Osher, Stanley J. $e degree supervisor.
720 1 $a Yin, Wotao $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0031
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32045196