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Multisection: parallelized bisection

Published: 07 December 2014 Publication History

Abstract

We consider a one-dimensional bisection method for finding the zero of a function, where function evaluations can be performed asynchronously in a parallel computing environment. Using dynamic programming, we characterize the Bayes-optimal policy for sequentially choosing points at which to query the function. In choosing these points, we face a trade-off between aggressively reducing the search space in the short term, and maintaining a desirable spread of queries in the long-term. Our results provide insight on how this trade-off is affected by function evaluation times, risk preferences, and computational budget.

References

[1]
Hernández-Lerma, O., and J. B. Lasserre. 1996. Discrete-time Markov control processes. Springer.
[2]
Kiefer, J. 1953. "Sequential minimax search for a maximum". Proceedings of the American Mathematical Society 4 (3): 502--506.
[3]
Powell, W. B. 2011. Approximate Dynamic Programming: Solving the Curses of Dimensionality, Volume 842. John Wiley & Sons.

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cover image ACM Conferences
WSC '14: Proceedings of the 2014 Winter Simulation Conference
December 2014
4032 pages

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IEEE Press

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Published: 07 December 2014

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  • Research-article

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WSC '14
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WSC '14: Winter Simulation Conference
December 7 - 10, 2014
Georgia, Savannah

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WSC '14 Paper Acceptance Rate 205 of 320 submissions, 64%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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