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We propose a framework and specific algorithms for screening a large (perhaps countably infinite) spaceof feasible solutions to generate a subset containing the optimal solution with high confidence. We attainthis goal even when only a small fraction of the feasible solutions are simulated. To accomplish it weexploit structural information about the space of functions within which the true objective function lies, andthen assess how compatible optimality is for each feasible solution with respect to the observed simulation outputs and the assumed function space. The result is a set of plausible optima. This approach can be viewed as a way to avoid slow simulation by leveraging fast optimization. Explicit formulations of the general approach are provided when the space of functions is either Lipschitz or convex. We establish both small- and large-sample properties of the approach, and provide two numerical examples.
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PLAUSIBLE INFERENCE WITH A PLAUSIBLE LIPSCHITZ CONSTANT
Plausible inference is a growing body of literature that treats stochastic simulation as a gray box when structural properties of the simulation output performance measures as a function of design, decision or contextual variables are known. Plausible inference exploits these properties to allow the outputs from values of decision variables that have been simulated to provide inference about output performance measures at values of decision variables that have not been simulated; statements about the possible optimality or feasibility are examples. Lipschitz continuity is a structural property of many simulation problems. Unfortunately, the all-important—and essential for plausible inference—Lipschitz constant is rarely known. In this paper we show how to obtain plausible inference with an estimated Lipschitz constant that is also derived by plausible inference reasoning, as well as how to create the experiment design to simulate.
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- Award ID(s):
- 2206973
- PAR ID:
- 10608097
- Editor(s):
- Lam, H; Azar, E; Batur, D; Gao, S; Xie, W; Hunter, SR; Rossetti, MD
- Publisher / Repository:
- Proceedings of the 2024 Winter Simulation Conference
- Date Published:
- Page Range / eLocation ID:
- 3554-3565
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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