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Statistical Learning for Probability-Constrained Stochastic Optimal Control
Optimization and Control · Submitted 30 Apr 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our algorithms offer an efficient and reliable extension of RMC to probability-constrained control.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. | contribution 0.88 | 0.79 | 0.04 | asserted 0.74 |
| s1 | Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while maintaining low probability of blackouts. | background 1.00 | 0.17 | 0.02 | asserted 0.98 |
| s2 | 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. | background 0.42 | 0.29 | 0.03 | asserted 0.53 |
| s3 | 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. | method 0.81 | 0.91 | 0.07 | asserted 1.00 |
| s4 | Our results indicate that using logistic or Gaussian process regression to estimate the admissibility probability outperforms the other options. | result 1.00 | 0.96 | 0.47 | hedged possibility 0.86 |
| s5 | Our algorithms offer an efficient and reliable extension of RMC to probability-constrained control. | interpretation 0.68 | 0.82 | 0.56 | asserted 1.00 |
| s6 | We illustrate our findings with two case studies for the microgrid problem. | contribution 0.66 | 0.88 | 0.05 | asserted 0.99 |
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The paper
Original 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.
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1 arXiv paper cite this in 1 sentence
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Builds on 1 paper
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This was extended for storage problems and controlled state process in [ref] .
Regress-Later Monte Carlo for Optimal Inventory Control with applications in energy · Regression Monte Carlo · 0.81
Cites as background 2 papers
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Among the approaches for approximating $f$ we mention [ref] and [ref] who exploit the structure of the problem to reduce the dimensionality of the regressions, [ref] who harness the distribution of process to reduce the variance of $f̂$ and [ref] who use non-parametric regression methods for $f̂$.
Regress-Later Monte Carlo for Optimal Inventory Control with applications in energy · Regression Monte Carlo · 0.83
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Among the approaches for approximating $f$ we mention [ref] and [ref] who exploit the structure of the problem to reduce the dimensionality of the regressions, [ref] who harness the distribution of process to reduce the variance of $f̂$ and [ref] who use non-parametric regression methods for $f̂$.
A Systematic Survey of the Effects of Wind Mass Loss Algorithms on the Evolution of Single Massive Stars · Regression Monte Carlo · 0.83
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