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Stochastic Methods in Optimization and Machine Learning

Bibliographic Details
Title: Stochastic Methods in Optimization and Machine Learning
Authors: Li, Fengpei
Publication Year: 2021
Collection: Columbia University: Academic Commons
Subject Terms: Operations research, Artificial intelligence, Machine learning, Stochastic processes--Computer programs
Description: Stochastic methods are indispensable to the modeling, analysis and design of complex systems involving randomness. In this thesis, we show how simulation techniques and simulation-based computational methods can be applied to a wide spectrum of applied domains including engineering, optimization and machine learning. Moreover, we show how analytical tools in statistics and computer science including empirical processes, probably approximately correct learning, and hypothesis testing can be used in these contexts to provide new theoretical results. In particular, we apply these techniques and present how our results can create new methodologies or improve upon existing state-of-the-art in three areas: decision making under uncertainty (chance-constrained programming, stochastic programming), machine learning (covariate shift, reinforcement learning) and estimation problems arising from optimization (gradient estimate of composite functions) or stochastic systems (solution of stochastic PDE). The work in the above three areas will be organized into six chapters, where each area contains two chapters. In Chapter 2, we study how to obtain feasible solutions for chance-constrained programming using data-driven, sampling-based scenario optimization (SO) approach. When the data size is insufficient to statistically support a desired level of feasibility guarantee, we explore how to leverage parametric information, distributionally robust optimization and Monte Carlo simulation to obtain a feasible solution of chance-constrained programming in small-sample situations. In Chapter 3, We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse. We utilize results from the Vapnik-Chervonenkis (VC) dimension and Probably Approximately Correct learning to provide a general framework. In Chapter 4, we design a robust importance re-weighting method for estimation/learning problem in the ...
Document Type: thesis
Language: English
DOI: 10.7916/d8-ngq8-9s10
Availability: https://doi.org/10.7916/d8-ngq8-9s10
Accession Number: edsbas.61CFC498
Database: BASE
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  – Url: https://doi.org/10.7916/d8-ngq8-9s10#
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  Data: Stochastic Methods in Optimization and Machine Learning
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Fengpei%22">Li, Fengpei</searchLink>
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  Data: 2021
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  Data: Columbia University: Academic Commons
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  Data: <searchLink fieldCode="DE" term="%22Operations+research%22">Operations research</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+intelligence%22">Artificial intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes--Computer+programs%22">Stochastic processes--Computer programs</searchLink>
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  Data: Stochastic methods are indispensable to the modeling, analysis and design of complex systems involving randomness. In this thesis, we show how simulation techniques and simulation-based computational methods can be applied to a wide spectrum of applied domains including engineering, optimization and machine learning. Moreover, we show how analytical tools in statistics and computer science including empirical processes, probably approximately correct learning, and hypothesis testing can be used in these contexts to provide new theoretical results. In particular, we apply these techniques and present how our results can create new methodologies or improve upon existing state-of-the-art in three areas: decision making under uncertainty (chance-constrained programming, stochastic programming), machine learning (covariate shift, reinforcement learning) and estimation problems arising from optimization (gradient estimate of composite functions) or stochastic systems (solution of stochastic PDE). The work in the above three areas will be organized into six chapters, where each area contains two chapters. In Chapter 2, we study how to obtain feasible solutions for chance-constrained programming using data-driven, sampling-based scenario optimization (SO) approach. When the data size is insufficient to statistically support a desired level of feasibility guarantee, we explore how to leverage parametric information, distributionally robust optimization and Monte Carlo simulation to obtain a feasible solution of chance-constrained programming in small-sample situations. In Chapter 3, We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse. We utilize results from the Vapnik-Chervonenkis (VC) dimension and Probably Approximately Correct learning to provide a general framework. In Chapter 4, we design a robust importance re-weighting method for estimation/learning problem in the ...
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      – SubjectFull: Artificial intelligence
        Type: general
      – SubjectFull: Machine learning
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      – SubjectFull: Stochastic processes--Computer programs
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      – TitleFull: Stochastic Methods in Optimization and Machine Learning
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              Y: 2021
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