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Convex Optimization and Implicit Differentiation Methods for Control and Estimation.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convex Optimization and Implicit Differentiation Methods for Control and Estimation./
作者:	Barratt, Shane Thomas.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	127 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Maps. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28812878
ISBN:	9798494454034

Convex Optimization and Implicit Differentiation Methods for Control and Estimation.
Barratt, Shane Thomas.

Convex Optimization and Implicit Differentiation Methods for Control and Estimation. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 127 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--Stanford University, 2021.

This item must not be sold to any third party vendors.

This disseration covers five applications of convex optimization [63] and implicit di↵erentiation methods [92] to the fields of control and estimation. Chapter 2 is based on the paper [8], co-authored with Akshay Agrawal, Stephen Boyd, Enzo Busseti, and Walaa Moursi. In this chapter, we consider the problem of eciently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly di↵erentiating the residual map for its homogeneous self-dual embedding, and solving the linear systems of equations required using an iterative method. This allows us to eciently compute the derivative operator, and its adjoint, evaluated at a vector. These correspond to computing an approximate new solution, given a perturbation to the cone program coecients (i.e., perturbation analysis), and to computing the gradient of a function of the solution with respect to the coecients. Our method scales to large problems, with numbers of coecients in the millions. We present an open-source Python implementation of our method that solves a cone program and returns the derivative and its adjoint as abstract linear maps; our implementation can be easily integrated into software systems for automatic di↵erentiation. Chapter 3 is based on the paper [31], co-authored with Stephen Boyd. In this chapter, we consider the problem of fitting the parameters in a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an ecient method to solve it based on sparse linear algebra. We then introduce the Kalman smoother tuning problem, which seeks to find parameters that achieve low prediction error on held out measurements. We derive a Kalman smoother auto-tuning algorithm, which is based on the proximal gradient method, that finds good, if not the best, parameters for a given dataset. Central to our method is the computation of the gradient of the prediction error on the held out measurements with respect to the parameters of the Kalman smoother; we describe how to compute this at little to no additional cost. We demonstrate the method on population migration within the United States as well as data collected from a smartphone's IMU+GPS system while driving.

ISBN: 9798494454034Subjects--Topical Terms:

544078
Maps.

Convex Optimization and Implicit Differentiation Methods for Control and Estimation.
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520 $a This disseration covers five applications of convex optimization [63] and implicit di↵erentiation methods [92] to the fields of control and estimation. Chapter 2 is based on the paper [8], co-authored with Akshay Agrawal, Stephen Boyd, Enzo Busseti, and Walaa Moursi. In this chapter, we consider the problem of eciently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly di↵erentiating the residual map for its homogeneous self-dual embedding, and solving the linear systems of equations required using an iterative method. This allows us to eciently compute the derivative operator, and its adjoint, evaluated at a vector. These correspond to computing an approximate new solution, given a perturbation to the cone program coecients (i.e., perturbation analysis), and to computing the gradient of a function of the solution with respect to the coecients. Our method scales to large problems, with numbers of coecients in the millions. We present an open-source Python implementation of our method that solves a cone program and returns the derivative and its adjoint as abstract linear maps; our implementation can be easily integrated into software systems for automatic di↵erentiation. Chapter 3 is based on the paper [31], co-authored with Stephen Boyd. In this chapter, we consider the problem of fitting the parameters in a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an ecient method to solve it based on sparse linear algebra. We then introduce the Kalman smoother tuning problem, which seeks to find parameters that achieve low prediction error on held out measurements. We derive a Kalman smoother auto-tuning algorithm, which is based on the proximal gradient method, that finds good, if not the best, parameters for a given dataset. Central to our method is the computation of the gradient of the prediction error on the held out measurements with respect to the parameters of the Kalman smoother; we describe how to compute this at little to no additional cost. We demonstrate the method on population migration within the United States as well as data collected from a smartphone's IMU+GPS system while driving.
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