Nonparametric density estimation for stochastic optimization with an observable state variable

Lauren A. Hannah, Warren Buckler Powell, David M. Blei

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

In this paper we study convex stochastic optimization problems where a noisy objective function value is observed after a decision is made. There are many stochastic optimization problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state s. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel based weights and Dirichlet process based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 23
Subtitle of host publication24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
StatePublished - Dec 1 2010
Event24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada
Duration: Dec 6 2010Dec 9 2010

Publication series

NameAdvances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Other

Other24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
CountryCanada
CityVancouver, BC
Period12/6/1012/9/10

All Science Journal Classification (ASJC) codes

  • Information Systems

Cite this

Hannah, L. A., Powell, W. B., & Blei, D. M. (2010). Nonparametric density estimation for stochastic optimization with an observable state variable. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).