英文标题：
《Statistical Learning for Probability-Constrained Stochastic Optimal
Control》
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作者：
Alessandro Balata and Michael Ludkovski and Aditya Maheshwari and Jan
Palczewski
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最新提交年份：
2020
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英文摘要：
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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中文摘要：
我们研究了基于蒙特卡罗的算法来解决具有概率约束的随机控制问题。我们的动机来自微电网管理，在微电网管理中，控制器试图以最佳方式调度柴油发电机，同时保持低停电概率。我们研究的关键问题是通过对系统状态的概率约束来学习隐含指定的容许控制集的经验模拟过程。我们提出了各种相关的统计工具，包括logistic回归、高斯过程回归、分位数回归和支持向量机，然后将其纳入近似动态规划的总体回归蒙特卡罗（RMC）框架。我们的结果表明，使用logistic或Gaussian过程回归估计可接受概率优于其他选项。我们的算法将RMC有效、可靠地推广到概率约束控制。我们用两个微电网问题的案例研究来说明我们的发现。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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