  "Weakly coupled dynamic program" describes a broad class of stochastic
optimization problems in which multiple controlled stochastic processes evolve
independently but subject to a set of linking constraints imposed on the
controls. One feature of the weakly coupled dynamic program is that it
decouples into lower-dimensional dynamic programs by dualizing the linking
constraint via the Lagrangian relaxation, which also yields a bound on the
optimal value of the original dynamic program. Together with the Lagrangian
bound, we utilize the information relaxation approach that relaxes the
non-anticipative constraint on the controls to obtain a tighter dual bound. We
also investigate other combinations of the relaxations and place the resulting
bounds in order. To tackle large-scale problems, we further propose a
computationally tractable method based on information relaxation, and provide
insightful interpretation and performance guarantee. We implement our method
and demonstrate its use through two numerical examples.
