The generator gradient estimator is an adjoint state method for stochastic differential equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914891598659584 |
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| author | Badolle, Quentin Gupta, Ankit Khammash, Mustafa |
| author_facet | Badolle, Quentin Gupta, Ankit Khammash, Mustafa |
| contents | Motivated by the increasing popularity of overparameterized Stochastic Differential Equations (SDEs) like Neural SDEs, Wang, Blanchet and Glynn recently introduced the generator gradient estimator, a novel unbiased stochastic gradient estimator for SDEs whose computation time remains stable in the number of parameters. In this note, we demonstrate that this estimator is in fact an adjoint state method, an approach which is known to scale with the number of states and not the number of parameters in the case of Ordinary Differential Equations (ODEs). In addition, we show that the generator gradient estimator is a close analogue to the exact Integral Path Algorithm (eIPA) estimator which was introduced by Gupta, Rathinam and Khammash for a class of Continuous-Time Markov Chains (CTMCs) known as stochastic chemical reactions networks (CRNs). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generator gradient estimator is an adjoint state method for stochastic differential equations Badolle, Quentin Gupta, Ankit Khammash, Mustafa Optimization and Control Probability Machine Learning Motivated by the increasing popularity of overparameterized Stochastic Differential Equations (SDEs) like Neural SDEs, Wang, Blanchet and Glynn recently introduced the generator gradient estimator, a novel unbiased stochastic gradient estimator for SDEs whose computation time remains stable in the number of parameters. In this note, we demonstrate that this estimator is in fact an adjoint state method, an approach which is known to scale with the number of states and not the number of parameters in the case of Ordinary Differential Equations (ODEs). In addition, we show that the generator gradient estimator is a close analogue to the exact Integral Path Algorithm (eIPA) estimator which was introduced by Gupta, Rathinam and Khammash for a class of Continuous-Time Markov Chains (CTMCs) known as stochastic chemical reactions networks (CRNs). |
| title | The generator gradient estimator is an adjoint state method for stochastic differential equations |
| topic | Optimization and Control Probability Machine Learning |
| url | https://arxiv.org/abs/2407.20196 |