Statistical Learning for Probability-Constrained Stochastic Optimal Control
Statistical Learning for Probability-Constrained Stochastic Optimal Control
复制标题
概率约束随机最优控制的统计学习
DOI：
10.1016/j.ejor.2020.08.041
复制
发表时间：
2020
影响因子：
6.4
通讯作者：
Palczewski, Jan
中科院分区：
文献类型：
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作者：
Balata, Alessandro;Ludkovski, Michael;Maheshwari, Aditya;Palczewski, Jan
研究了基于蒙特卡罗算法求解具有局部概率约束的随机控制问题。我们的动机来自微电网管理，控制器试图在每一步保持低停电概率的情况下，优化调度柴油发电机。我们研究的关键问题是学习状态相关的可接受控制集的经验模拟程序，该控制集通过系统状态的概率约束隐式指定。我们提出了各种相关的统计工具，包括逻辑回归，高斯过程回归，分位数回归和支持向量机，然后我们将其纳入近似动态规划的整体回归蒙特卡罗（RMC）框架。我们的结果表明，使用逻辑或高斯过程回归来估计可接受概率优于其他选择。我们的算法提供了RMC到概率约束控制的有效和可靠的扩展。我们通过对微电网问题的两个案例研究来说明我们的发现。
We investigate Monte Carlo based algorithms for solving stochastic control problems with local probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while maintaining low probability of blackouts at each step. The key question we investigate are empirical simulation procedures for learning the state-dependent 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.