Stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous functional evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this work, we introduce an importance sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Our framework combines Markov chain Monte Carlo methods with kernel density estimation algorithms to build a nonparametric importance sampling distribution, which can then be used to produce a lower-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate variance, multimodal, or rare-event distributions.

This paper presents a computational model of verb acquisition which uses what we will call the principle of structured overcommitment to eliminate the need for negative evidence. The learner escapes from the need to be told that certain possibilities cannot occur (i.e., are "ungrammatical") by one simple expedient: It assumes that all properties it has observed are either obligatory or forbidden until it sees otherwise, at which point it decides that what it thought was either obligatory or forbidden is merely optional. This model is built upon a classification of verbs based upon a simple three-valued set of features which represents key aspects of a verb's syntactic structure, its predicate/argument structure, and the mapping between them.