Gradient Estimation Via Perturbation Analysis

By Paul Glasserman, Y. Ho. 1990

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Citations in the corpus

Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming (2013, methodology): “tion P. Typically this transformation results in a nonconvex integrand function. Other techniques have also been developed to compute unbiased estimators for the gradient of f(·) in (1.5) (see, e.g., [8, 13, 20, 35]). • Finally, in simulation-basedoptimization, the objective function is given by f(x”
Measure-Valued Differentiation for Markov Chains (2008, methodology): “Many real-world systems in manufacturing, transportation, communication networks, or finance can be modeled by general state-space Markov chains, such as generalized semi-Markov processes (see [1]).”
Sensitivity analysis of discrete event systems by the “push out” method (1992, background): “Glasserman [ 8 ]). In many important applications, however, the sample function L(y, 192) is either not everywhere differentiable in 192 or not available.”
Optimization for Simulation : Theory vs . Practice (2002, background): “…algorithms is dramatically enhanced with the availability of direct gradients, one motivating force behind the flurry of research in gradient estimation techniques in the 1990s (see the books by Fu and Hu 1997, Glasserman 1991, Ho and Cao 1991, Rubinstein and Shapiro 1993, Pflug 1996 ).”
Multi-product inventory planning with downward substitution, stochastic demand and setup costs (2004, methodology): “The IPA estimator for the (right) derivative of G(Y ) w.r.t. yj is cj plus the average value of the dual price of constraint (II) of Equation (4) corresponding to product j. Remark 1.”
Pricing American Options: A Comparison of Monte Carlo Simulation Approaches ⁄ (2001, methodology): “where Lj = L(θn + cj∆j , ω + j ), (21) Lj = L(θn − cj∆j , ω− j ), (22)”
Perturbation analysis for denumerable Markov chains with application to queueing models (2004, background): “(The results on regular perturbation can also be used for infinitesimal perturbation analysis [6], [12], [13], [14], [26].”
A Guide to Sample Average Approximation (2015, background): “This section also showcases the close connection between problems that are “SAA appropriate” and those that are amenable to infinitesimal perturbation analysis (IPA) [13, 17] for gradient estimation.”
Stochastic Optimization (2003, methodology): “We refer the interested reader to Glasserman (1991) and Ho and Cao (1991) for a thorough discussion of that topic.”
Optimization for Simulation: Theory vs. Practice (2002, background): “flurry of research in gradient estimation techniques in the 1990s (see the books by Fu and Hu 1997, Glasserman 1991, Ho and Cao 1991, Rubinstein and Shapiro 1993, Pflug1996).”
Monte Carlo Gradient Estimation in Machine Learning (2019, background): “Other variations of perturbation analysis expand its applicability, see Suri and Zazanis (1988) and the books by Glasserman and Ho (1991) and Ho and Cao (2012).”
Monte Carlo sampling-based methods for stochastic optimization (2014, background): “Classical treatment of such problems can be found in Glasserman [86], Rubinstein and Shapiro [210], Pflug [190] and Fu and Hu [83], see also Robinson [201] and Homem-de-Mello [107] for the case where the function g(·) is non-differentiable.”
Sensitivity in risk analyses with uncertain numbers. (2006, background): “General approaches for sensitivity analysis of discrete event dynamic systems are studied by Ho and Cao (1991), Glasserman (1991), Rubinstein and Shapiro (1993), and Pflug (1996), inter alia.”
The general inefficiency of batch training for gradient descent learning (2003, background): “While it is true that YðWÞ is not equal to GðWÞ; the expected value of Y does equal G (under fairly modest regularity conditions) (Glasserman, 1991; Spall, 1999).”
Two Types of RG-Factorizations of Quasi-birth-and-death Processes and Their Applications to Stochastic Integral Functionals (2004, background): “Readers also may refer to Glasserman([12,13]) for more details.”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “To get the estimate ĥn, we can use the IPA estimator [124, 129, 136, 177], which is based on the identity”
Simulation-based optimization of Markov reward processes (1998, background): “This property is very helpful in producing simulation-based estimates of .”