Stochastic Gradient Estimation (book, handbook chapter) • Something New: Global Optimization Algorithm Output performance measures estimated via stochastic simulation that is EXPENSIVE, (nonlinear, possibly nondifferentiable) Inﬂnitesimal Perturbation Analysis. Analysis and Improvement of Policy Gradient Estimation Tingting Zhao, Hirotaka Hachiya, Gang Niu, and Masashi Sugiyama Tokyo Institute of Technology [email protected], [email protected], [email protected], [email protected] Abstract Policy gradient is a useful model-free reinforcement learning approach, but it tends to suffer from instability of gradient Cited by: 6. Analysis and Improvement of Policy Gradient Estimation 3 Problem Formulation Let us consider a Markov decision problem speciﬁed by (S,A,PT,PI,r,γ), where Sis aset of ℓ-dimensional continuous states, Ais a set of continuous actions, PT(s′|s,a) is the transition probability density from current state s to next state s′ when action ais taken, PI(s) is the probability of initial. Augmented Infinitesimal Perturbation Analysis is used to determine asymptotically unbiased and strong consistent gradient estimates for use in the capacity planning of intree ATM networks. These gradients are used to determine the locally optimal minimum average network delay by applying a steepest descent algorithm with projection and an Armijo line search to .

Stochastic Approximation (SA) and Gradient Estimation • Gradient Estimation: –e.g. Finite differences (easiest, but biased): make a small perturbation in each dimension –Others yield unbiased estimates in special cases. • Pros: Fast, works on (simple) constrained problemsFile Size: 3MB. provide a direct way of calculating gradient estimates. 1 INTRODUCTION Infinitesimal perturbation analysis (IPA) is a technique for estimating the gradient of a system performance measure by observing the sample path from a single simulation run (Ho et al. , Glasserman , Ho and Cao , Fu and Hu. Gradient and Grid Perturbation Grid Perturbation • In order to compute this contribution, regeneration of the grid is required based on perturbations on the surface. • The grid regeneration is needed for every surface perturbation. • This procedure can be costly if the geometry is three-dimensional and complex, and would have to be repeated a number of times proportional to theFile Size: KB. Perturbation Analysis of Optimization Problems J. Frederic Bonnans1 and Alexander Shapiro2 1INRIA-Rocquencourt, Domaine de Voluceau, B.P. , Rocquencourt, France, and Ecole Polytechnique, France 2School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia , USA.

their complexity analysis. This book is meant to be something in between, a book on general convex optimization that focuses on problem formulation and modeling. We should also mention what this book is not. It is not a text primarily about convex analysis, or the mathematics of convex optimization; several existing texts cover these topics well. Scaling up M-estimation via sampling designs: the Horvitz-Thompson stochastic gradient descent Asymptotic analysis of Horvitz-Thompson estimators based on survey data (see [1]) has received a good deal of attention, in particular in the context of mean estimation and regression. Many vibration problems in engineering are nonlinear in nature. The usual linear analysis may be inadequate for many applications. An essential difference in the study of nonlinear systems is that general solutions cannot be obtained by superposition, as in the case of linear systems. Moreover, the nonlinearity brings many new phenomena, which do not occur in linear systems. bation analysis (cf. Ho and Cao , Glasserman ). Even in the field ofperturbation analysis, dif ferent techniques have been developed. For gradient estimation, the "original" technique is infinitesimal perturbation analysis (IPA), which remains the eas iest PA technique to apply in practice. However, its.