论文标题
多阶段随机优化问题的时间一致性在预期中的限制下
Time Consistency for Multistage Stochastic Optimization Problems under Constraints in Expectation
论文作者
论文摘要
我们考虑了由时间（离散阶段）的多阶段随机优化问题的序列索引。在每个时间，家庭中的优化问题都会通过一些数量（初始状态，约束级别..。）进行参数。在此框架中，我们引入了一个适应时间的概念一致的最佳解决方案，即在过去截断后保持最佳的解决方案，并且对于参数的任何值都是最佳的。我们将这次的一致性概念与马尔可夫决策过程中的状态变量的概念联系起来，以在最终期望或概率上提出的一系列多阶段随机优化问题，这些问题结合了最终的状态约束。对于此类问题，当原始噪声随机过程独立于阶段并采用有限的值时，我们表明可以通过考虑有限的维态变量来获得时间一致的解决方案。我们说明了一个简单的大坝管理问题的结果。
We consider sequences-indexed by time (discrete stages)-of families of multistage stochastic optimization problems. At each time, the optimization problems in a family are parameterized by some quantities (initial states, constraint levels.. .). In this framework, we introduce an adapted notion of time consistent optimal solutions, that is, solutions that remain optimal after truncation of the past and that are optimal for any values of the parameters. We link this time consistency notion with the concept of state variable in Markov Decision Processes for a class of multistage stochastic optimization problems incorporating state constraints at the final time, either formulated in expectation or in probability. For such problems, when the primitive noise random process is stagewise independent and takes a finite number of values, we show that time consistent solutions can be obtained by considering a finite dimensional state variable. We illustrate our results on a simple dam management problem.
