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The first step in solving a stochastic optimization problem is providing a mathematical model. How the problem is modeled can impact the solution strategy. In this chapter, we provide a flexible modeling framework that uses a classic control-theoretic framework, avoiding devices such as one-step transition matrices. We describe the five fundamental elements… (More)

- Jennie Si, Andy Barto, Warren Powell, Donald Wunsch, George G. Lendaris, James C. Neidhoefer +2 others
- 2004

We consider a class of problems of scheduling n jobs on m identical, uniform, or unrelated parallel machines with an objective of minimizing an additive criterion. We propose a decomposition approach for solving these problems exactly. The decomposition approach rst formulates these problems as an integer program, and then reformulates the integer program,… (More)

We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives' mean values, algorithms may utilize this dependence to perform efficiently even when the… (More)

We address the problem of determining optimal stepsizes for estimating parameters in the context of approximate dynamic programming. The sufficient conditions for convergence of the stepsize rules have been known for 50 years, but practical computational work tends to use formulas with parameters that have to be tuned for specific applications. The problem… (More)

W e consider a stochastic version of a dynamic resource allocation problem. In this setting , reusable resources must be assigned to tasks that arise randomly over time. We solve the problem using an adaptive dynamic programming algorithm that uses nonlinear functional approximations that give the value of resources in the future. Our functional… (More)

In a sequential Bayesian ranking and selection problem with independent normal populations and common known variance, we study a previously introduced measurement policy which we refer to as the knowledge-gradient policy. This policy myopically maximizes the expected increment in the value of information in each time period, where the value is measured… (More)

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the… (More)