# Statistical Learning for Probability-Constrained Stochastic Optimal Control

## TL;DR

This paper develops Monte Carlo algorithms using statistical learning methods like logistic and Gaussian process regression to solve stochastic control problems with probabilistic constraints, demonstrated on microgrid management.

## Contribution

It introduces a Regression Monte Carlo framework incorporating statistical tools for learning admissible control sets under probabilistic constraints, improving efficiency and reliability.

## Key findings

- Logistic and Gaussian process regression outperform other methods in estimating admissibility probabilities.
- The proposed algorithms extend RMC to handle probability constraints effectively.
- Case studies validate the approach in microgrid control scenarios.

## Abstract

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.