Time Consistency for Multistage Stochastic Optimization Problems under Constraints in Expectation
研究了多阶段随机优化问题中时间一致最优解的概念，将其与马尔可夫决策过程的状态变量联系起来，并在噪声独立且有限取值时证明了可通过有限维状态变量获得时间一致解。
We consider sequences-indexed by time (discrete stages)-of families of\nmultistage stochastic optimization problems. At each time, the optimization\nproblems in a family are parameterized by some quantities (initial states,\nconstraint levels.. .). In this framework, we introduce an adapted notion of\ntime consistent optimal solutions, that is, solutions that remain optimal after\ntruncation of the past and that are optimal for any values of the parameters.\nWe link this time consistency notion with the concept of state variable in\nMarkov Decision Processes for a class of multistage stochastic optimization\nproblems incorporating state constraints at the final time, either formulated\nin expectation or in probability. For such problems, when the primitive noise\nrandom process is stagewise independent and takes a finite number of values, we\nshow that time consistent solutions can be obtained by considering a finite\ndimensional state variable. We illustrate our results on a simple dam\nmanagement problem.\n