论文标题
数据驱动的非参数鲁棒控制在依赖性不确定性下
Data-Driven Nonparametric Robust Control under Dependence Uncertainty
论文作者
论文摘要
我们考虑了一个多周期随机控制问题，其中系统的多元驱动随机因子已知边缘分布，但依赖性结构不确定。为了解决问题，我们建议实施非参数自适应鲁棒控制框架。我们的目标是通过一系列不断观察数据产生的不确定性集找到对最坏情况的最佳控制。然后，我们使用随机梯度下降算法来数值处理相应的高维动态INF-SUP优化问题。我们在效用最大化的背景下介绍了数值结果，并表明控制器受益于了解有关不确定模型的更多信息。
We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the nonparametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model.
