  In this paper we study convex stochastic search problems where a noisy
objective function value is observed after a decision is made. There are many
stochastic search 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. 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.
