Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System

Marvin K. Nakayama; Bruno Tuffin

doi:10.1109/WSC57314.2022.10015238

Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System

Marvin K. Nakayama, Bruno Tuffin

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hitting-time distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.

Original language	English (US)
Title of host publication	Proceedings of the 2022 Winter Simulation Conference, WSC 2022
Editors	B. Feng, G. Pedrielli, Y. Peng, S. Shashaani, E. Song, C.G. Corlu, L.H. Lee, E.P. Chew, T. Roeder, P. Lendermann
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	121-132
Number of pages	12
ISBN (Electronic)	9798350309713
DOIs	https://doi.org/10.1109/WSC57314.2022.10015238
State	Published - 2022
Event	2022 Winter Simulation Conference, WSC 2022 - Guilin, China Duration: Dec 11 2022 → Dec 14 2022

Publication series

Name	Proceedings - Winter Simulation Conference
Volume	2022-December
ISSN (Print)	0891-7736

Conference

Conference	2022 Winter Simulation Conference, WSC 2022
Country/Territory	China
City	Guilin
Period	12/11/22 → 12/14/22

All Science Journal Classification (ASJC) codes

Software
Modeling and Simulation
Computer Science Applications

Access to Document

10.1109/WSC57314.2022.10015238

Cite this

Nakayama, M. K., & Tuffin, B. (2022). Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System. In B. Feng, G. Pedrielli, Y. Peng, S. Shashaani, E. Song, C. G. Corlu, L. H. Lee, E. P. Chew, T. Roeder, & P. Lendermann (Eds.), Proceedings of the 2022 Winter Simulation Conference, WSC 2022 (pp. 121-132). (Proceedings - Winter Simulation Conference; Vol. 2022-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC57314.2022.10015238

Nakayama, Marvin K. ; Tuffin, Bruno. / Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System. Proceedings of the 2022 Winter Simulation Conference, WSC 2022. editor / B. Feng ; G. Pedrielli ; Y. Peng ; S. Shashaani ; E. Song ; C.G. Corlu ; L.H. Lee ; E.P. Chew ; T. Roeder ; P. Lendermann. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 121-132 (Proceedings - Winter Simulation Conference).

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title = "Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System",

abstract = "For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hitting-time distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.",

author = "Nakayama, {Marvin K.} and Bruno Tuffin",

note = "Funding Information: MARVIN K. NAKAYAMA is a professor in the Department of Computer Science at the New Jersey Institute of Technology. He received an M.S. and Ph.D. in operations research from Stanford University and a B.A. in mathematics-computer science from U.C. San Diego. He is a recipient of a CAREER Award from the National Science Foundation, and a paper he co-authored received the Best Theoretical Paper Award for the 2014 Winter Simulation Conference. He is an associate editor for ACM Transactions on Modeling and Computer Simulation, and served as the simulation area editor for the INFORMS Journal on Computing from 2007–2016. His research interests include simulation, modeling, statistics, risk analysis, and energy. His email address is marvin@njit.edu. Publisher Copyright: {\textcopyright} 2022 IEEE.; 2022 Winter Simulation Conference, WSC 2022 ; Conference date: 11-12-2022 Through 14-12-2022",

year = "2022",

doi = "10.1109/WSC57314.2022.10015238",

language = "English (US)",

series = "Proceedings - Winter Simulation Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "121--132",

editor = "B. Feng and G. Pedrielli and Y. Peng and S. Shashaani and E. Song and C.G. Corlu and L.H. Lee and E.P. Chew and T. Roeder and P. Lendermann",

booktitle = "Proceedings of the 2022 Winter Simulation Conference, WSC 2022",

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}

Nakayama, MK & Tuffin, B 2022, Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System. in B Feng, G Pedrielli, Y Peng, S Shashaani, E Song, CG Corlu, LH Lee, EP Chew, T Roeder & P Lendermann (eds), Proceedings of the 2022 Winter Simulation Conference, WSC 2022. Proceedings - Winter Simulation Conference, vol. 2022-December, Institute of Electrical and Electronics Engineers Inc., pp. 121-132, 2022 Winter Simulation Conference, WSC 2022, Guilin, China, 12/11/22. https://doi.org/10.1109/WSC57314.2022.10015238

Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System. / Nakayama, Marvin K.; Tuffin, Bruno.
Proceedings of the 2022 Winter Simulation Conference, WSC 2022. ed. / B. Feng; G. Pedrielli; Y. Peng; S. Shashaani; E. Song; C.G. Corlu; L.H. Lee; E.P. Chew; T. Roeder; P. Lendermann. Institute of Electrical and Electronics Engineers Inc., 2022. p. 121-132 (Proceedings - Winter Simulation Conference; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Nakayama, Marvin K.

AU - Tuffin, Bruno

N1 - Funding Information: MARVIN K. NAKAYAMA is a professor in the Department of Computer Science at the New Jersey Institute of Technology. He received an M.S. and Ph.D. in operations research from Stanford University and a B.A. in mathematics-computer science from U.C. San Diego. He is a recipient of a CAREER Award from the National Science Foundation, and a paper he co-authored received the Best Theoretical Paper Award for the 2014 Winter Simulation Conference. He is an associate editor for ACM Transactions on Modeling and Computer Simulation, and served as the simulation area editor for the INFORMS Journal on Computing from 2007–2016. His research interests include simulation, modeling, statistics, risk analysis, and energy. His email address is marvin@njit.edu. Publisher Copyright: © 2022 IEEE.

PY - 2022

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N2 - For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hitting-time distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.

AB - For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hitting-time distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.

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BT - Proceedings of the 2022 Winter Simulation Conference, WSC 2022

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A2 - Shashaani, S.

A2 - Song, E.

A2 - Corlu, C.G.

A2 - Lee, L.H.

A2 - Chew, E.P.

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A2 - Lendermann, P.

PB - Institute of Electrical and Electronics Engineers Inc.

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ER -

Nakayama MK, Tuffin B. Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System. In Feng B, Pedrielli G, Peng Y, Shashaani S, Song E, Corlu CG, Lee LH, Chew EP, Roeder T, Lendermann P, editors, Proceedings of the 2022 Winter Simulation Conference, WSC 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 121-132. (Proceedings - Winter Simulation Conference). doi: 10.1109/WSC57314.2022.10015238

Density Estimators of the Cumulative Reward Up to a Hitting Time to a Rarely Visited Set of a Regenerative System

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