Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We explore how nonlinear control algorithms, often employing line...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2024-11-01
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| Series: | Open Journal of Mathematical Optimization |
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| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.32/ |
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| author | Roulet, Vincent Srinivasa, Siddhartha Fazel, Maryam Harchaoui, Zaid |
| author_facet | Roulet, Vincent Srinivasa, Siddhartha Fazel, Maryam Harchaoui, Zaid |
| author_sort | Roulet, Vincent |
| collection | DOAJ |
| description | Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We explore how nonlinear control algorithms, often employing linear and/or quadratic approximations, can be effectively cast within this framework. Our approach illuminates shared components and differences between gradient descent, Gauss–Newton, Newton, and differential dynamic programming methods in the context of discrete time nonlinear control. Furthermore, we present line-search strategies and regularized variants of these algorithms, along with a comprehensive analysis of their computational complexities. We study the performance of the aforementioned algorithms on various nonlinear control benchmarks, including autonomous car racing simulations using a simplified car model. All implementations are publicly available in a package coded in a differentiable programming language. |
| format | Article |
| id | doaj-art-d92a8fcfd78544d6bcac856ae3bc72c0 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-d92a8fcfd78544d6bcac856ae3bc72c02025-02-07T14:01:17ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602024-11-01516310.5802/ojmo.3210.5802/ojmo.32Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic TemplatesRoulet, Vincent0Srinivasa, Siddhartha1Fazel, Maryam2Harchaoui, Zaid3Google Brain, Seattle, USA (Work completed at the University of Washington before joining Google)Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, USADepartment of Electrical and Computer Engineering, University of Washington, Seattle, USADepartment of Statistics University of Washington, Seattle, USAIterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We explore how nonlinear control algorithms, often employing linear and/or quadratic approximations, can be effectively cast within this framework. Our approach illuminates shared components and differences between gradient descent, Gauss–Newton, Newton, and differential dynamic programming methods in the context of discrete time nonlinear control. Furthermore, we present line-search strategies and regularized variants of these algorithms, along with a comprehensive analysis of their computational complexities. We study the performance of the aforementioned algorithms on various nonlinear control benchmarks, including autonomous car racing simulations using a simplified car model. All implementations are publicly available in a package coded in a differentiable programming language.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.32/Nonlinear Discrete Time ControlDifferentiable ProgrammingNewtonGauss–NewtonDynamic Differentiable Programming |
| spellingShingle | Roulet, Vincent Srinivasa, Siddhartha Fazel, Maryam Harchaoui, Zaid Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates Open Journal of Mathematical Optimization Nonlinear Discrete Time Control Differentiable Programming Newton Gauss–Newton Dynamic Differentiable Programming |
| title | Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates |
| title_full | Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates |
| title_fullStr | Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates |
| title_full_unstemmed | Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates |
| title_short | Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates |
| title_sort | iterative linear quadratic optimization for nonlinear control differentiable programming algorithmic templates |
| topic | Nonlinear Discrete Time Control Differentiable Programming Newton Gauss–Newton Dynamic Differentiable Programming |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.32/ |
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