2022/08/29 by Pierre Carpentier, Carpentier, Pierre, Jean‐Philippe Chancelier +3
Computer Science · Decision Sciences · Engineering · #Bayesian Modeling and Causal Inference #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Water resources management and optimization
paper · doi:10.48550/arxiv.2208.13522
openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.