Bounds for Multistage Stochastic Programs Using Supervised Learning Strategies

We propose a generic method for obtaining quickly good upper bounds on the minimal value of a multistage stochastic program. The method is based on the simulation of a feasible decision policy, synthesized by a strategy relying on any scenario tree approximation from stochastic programming and on supervised learning techniques from machine learning. 1 Context Let Ω denote a measurable space equipped with a sigma algebra B of subsets of Ω, defined as follows. For t = 0, 1, . . . , T − 1, we let ξt be a random variable valued in a subset of an Euclidian space Ξt, and let Bt denote the sigma algebra generated by the collection of random variables ξ[0: t−1] def = {ξ0, . . . , ξt−1}, with B0 = {∅, Ω} corresponding to the trivial sigma algebra. Then we set BT −1 = B. Note that B0 ⊂ B1 ⊂ · · · ⊂ BT −1 form a filtration; without loss of generality, we can assume that the inclusions are proper — that is, ξt cannot be reduced to a function of ξ[0: t−1]. Le...

• Type: Conference
• Year: 2009
• Where: SAGA
• Authors: Boris Defourny, Damien Ernst, Louis Wehenkel
• Keywords: Control Systems, Measurable Space, SAGA 2009, Sigma Algebra, Space