Lauren Hannah

ICML Conference 2012 Conference Paper

Ensemble Methods for Convex Regression with Applications to Geometric Programming Based Circuit Design

• Lauren Hannah
• David B. Dunson

ICML Conference 2011 Conference Paper

Approximate Dynamic Programming for Storage Problems

• Lauren Hannah
• David B. Dunson

NeurIPS Conference 2010 Conference Paper

Nonparametric Density Estimation for Stochastic Optimization with an Observable State Variable

• Lauren Hannah
• Warren Powell
• David Blei

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 for the joint distribution of state-outcome pairs to create weights for previous observations. The weights effectively group similar states. Those similar to the current state are used to create a convex, deterministic approximation of the objective function. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We offer 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 Dirichlet process weights can offer substantial benefits over kernel based weights and, more generally, that nonparametric estimation methods provide good solutions to otherwise intractable problems.