论文标题
受模型不确定性的风险过滤和规避风险的控制
Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty
论文作者
论文摘要
我们考虑了马尔可夫决策过程，视为在贝叶斯框架中以模型不确定性为准，在那里我们假设观察到状态过程，但观察者的定律是未知的。此外，虽然在时间$ t $时观察到状态流程和控件，但可能取决于未知参数的实际成本在时间$ t $时不知道。控制器通过使用特殊风险措施的家族来优化总成本，我们称之为风险过滤器，并适当定义以考虑受控系统的模型不确定性。这些关键特征导致非标准和非平凡的风险控制问题，我们为此得出了最佳的钟声原则。我们在两个实际示例上说明了一般理论：最佳投资和临床试验。
We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the state process and the controls are observed at time $t$, the actual cost that may depend on the unknown parameter is not known at time $t$. The controller optimizes total cost by using a family of special risk measures, that we call risk filters and that are appropriately defined to take into account the model uncertainty of the controlled system. These key features lead to non-standard and non-trivial risk-averse control problems, for which we derive the Bellman principle of optimality. We illustrate the general theory on two practical examples: optimal investment and clinical trials.
