  We investigate Monte Carlo based algorithms for solving stochastic control
problems with probabilistic constraints. Our motivation comes from microgrid
management, where the controller tries to optimally dispatch a diesel generator
while maintaining low probability of blackouts. The key question we investigate
are empirical simulation procedures for learning the admissible control set
that is specified implicitly through a probability constraint on the system
state. We propose a variety of relevant statistical tools including logistic
regression, Gaussian process regression, quantile regression and support vector
machines, which we then incorporate into an overall Regression Monte Carlo
(RMC) framework for approximate dynamic programming. Our results indicate that
using logistic or Gaussian process regression to estimate the admissibility
probability outperforms the other options. Our algorithms offer an efficient
and reliable extension of RMC to probability-constrained control. We illustrate
our findings with two case studies for the microgrid problem.
