{"title":"通过似然比法进行高效嵌套模拟实验设计","authors":"Ben Mingbin Feng, Eunhye Song","doi":"10.1287/ijoc.2022.0392","DOIUrl":null,"url":null,"abstract":"<p>In the nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario’s conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bilevel optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mrow><mi mathvariant=\"script\">O</mi><mo stretchy=\"false\">(</mo><msup><mrow><mi mathvariant=\"normal\">Γ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">)</mo></mrow></math></span><span></span> mean squared error of the estimators given simulation budget <span><math altimg=\"eq-00002.gif\" display=\"inline\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.</p><p><b>History:</b> Accepted by Bruno Tuffin, Area Editor for Simulation.</p><p><b>Funding:</b> This work was supported by the National Science Foundation [Grant CMMI-2045400] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-03755].</p><p><b>Supplemental Material:</b> The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0392) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0392). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.</p>","PeriodicalId":13620,"journal":{"name":"Informs Journal on Computing","volume":"184 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method\",\"authors\":\"Ben Mingbin Feng, Eunhye Song\",\"doi\":\"10.1287/ijoc.2022.0392\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In the nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario’s conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bilevel optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\"><mrow><mi mathvariant=\\\"script\\\">O</mi><mo stretchy=\\\"false\\\">(</mo><msup><mrow><mi mathvariant=\\\"normal\\\">Γ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy=\\\"false\\\">)</mo></mrow></math></span><span></span> mean squared error of the estimators given simulation budget <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\"><mi mathvariant=\\\"normal\\\">Γ</mi></math></span><span></span>. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.</p><p><b>History:</b> Accepted by Bruno Tuffin, Area Editor for Simulation.</p><p><b>Funding:</b> This work was supported by the National Science Foundation [Grant CMMI-2045400] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-03755].</p><p><b>Supplemental Material:</b> The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0392) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0392). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.</p>\",\"PeriodicalId\":13620,\"journal\":{\"name\":\"Informs Journal on Computing\",\"volume\":\"184 1\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Informs Journal on Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1287/ijoc.2022.0392\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Informs Journal on Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1287/ijoc.2022.0392","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method
In the nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario’s conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bilevel optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves mean squared error of the estimators given simulation budget . Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.
History: Accepted by Bruno Tuffin, Area Editor for Simulation.
Funding: This work was supported by the National Science Foundation [Grant CMMI-2045400] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-03755].
Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0392) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0392). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.
期刊介绍:
The INFORMS Journal on Computing (JOC) is a quarterly that publishes papers in the intersection of operations research (OR) and computer science (CS). Most papers contain original research, but we also welcome special papers in a variety of forms, including Feature Articles on timely topics, Expository Reviews making a comprehensive survey and evaluation of a subject area, and State-of-the-Art Reviews that collect and integrate recent streams of research.