86 research outputs found

    Online Supplement to ‘Myopic Allocation Policy with Asymptotically Optimal Sampling Rate’

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    This document is the Online Supplement to ‘Myopic Allocation Policy with Asymptotically Optimal Sampling Rate,’ to be published in the IEEE Transactions of Automatic Control in 2017.In this online appendix, we test the performance of the AOMAP (asymptotically optimal myopic allocation policy) algorithm under the unknown variances scenario and compare it with EI (expected improvement) and OCBA (optimal computing budget allocation).This work was supported in part by the National Science Foundation (NSF) under Grants CMMI-1362303 and CMMI-1434419, by the Air Force of Scientific Research (AFOSR) under Grant FA9550-15-10050, by the National Natural Science Foundation of China (Project 11171256), and by the China Postdoctoral Science Foundation under Grant 2015M571495

    Generalized Likelihood Ratio Method for Stochastic Models with Uniform Random Numbers As Inputs

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    We propose a new unbiased stochastic gradient estimator for a family of stochastic models with uniform random numbers as inputs. By extending the generalized likelihood ratio (GLR) method, the proposed estimator applies to discontinuous sample performances with structural parameters without requiring that the tails of the density of the input random variables go down to zero smoothly, an assumption in Peng et al. (2018) and Peng et al. (2020a) that precludes a direct formulation in terms of uniform random numbers as inputs. By overcoming this limitation, our new estimator greatly expands the applicability of the GLR method, which we demonstrate for several general classes of uniform input random numbers, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new derivative estimator works in specific settings such as density estimation, distribution sensitivity for quantiles, and sensitivity analysis for Markov chain stopping time problems, which we illustrate with applications to statistical quality control, stochastic activity networks, and credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in sample performance