Nonparametric Density Estimation for Stochastic Optimization with an Observable State Variable

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. Those similar to the current state are used to create a convex, deterministic approximation of the objective function.