Sampling Bounds for Stochastic Optimization

A large class of stochastic optimization problems can be modeled as minimizing an objective function f that depends on a choice of a vector x ∈ X, as well as on a random external parameter ω ∈ Ω given by a probability distribution π. The value of the objective function is a random variable and often the goal is to find an x ∈ X to minimize the expected cost Eω[fω(x)]. Each ω is referred to as a scenario. We consider the case when Ω is large or infinite and we are allowed to sample from π in a black-box fashion. A common method, known as the SAA method (sample average approximation), is to pick sufficiently many independent samples from π and use them to approximate π and correspondingly Eω[fω(x)]. This is one of several scenario reduction methods used in practice. There has been substantial recent interest in two-stage stochastic versions of combinatorial optimization problems which can be modeled by the framework described above. In particular, we are interested ...

• Type: Conference
• Year: 2005
• Where: APPROX
• Authors: Moses Charikar, Chandra Chekuri, Martin Pál
• Keywords: Algorithms, APPROX 2005, Objective Function, Optimization Problems, SAA Method