Trajectory Following Dynamic Programming algorithms without finite support assumptions
Abstract
We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms,
that iteratively refines approximations of cost-to-go functions of multistage stochastic problems with independent
random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming
algorithm.
Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and
complexity proof that allows random variables with non-finitely supported distributions. In particular, this leads
to new complexity results for numerous known algorithms. Further, we detail how TFDP algorithms can be
implemented without the finite support assumption, either through approximations or exact computations.
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