Distribution-free algorithms for predictive stochastic programming in the presence of streaming data

Abstract

Abstract This paper studies a fusion of concepts from stochastic programming and non-parametric statistical learning in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of predictors (leading indicators). This paper studies two classes of methods for such joint prediction-optimization models. One of the methods may be classified as a first-order method, whereas the other studies piecewise linear approximations. Both of these methods are based on coupling non-parametric estimation for predictive purposes, and optimization for decision-making within one unified framework. In addition, our study incorporates several non-parametric estimation schemes, including k nearest neighbors ( k NN) and other standard kernel estimators. Our computational results demonstrate that the new algorithms proposed in this paper outperform traditional approaches which were not designed for streaming data applications requiring simultaneous estimation and optimization as important design features for such algorithms. For instance, coupling k NN with Stochastic Decomposition (SD) turns out to be over 40 times faster than an online version of Benders Decomposition while finding decisions of similar quality. Such computational results motivate a paradigm shift in optimization algorithms that are intended for modern streaming applications.