  In this paper, we consider two sequential decision making problems with a
convexity structure, namely an energy storage optimization task and a
multi-product assembly example. We formulate these problems in the stochastic
programming framework and discuss an approximate dynamic programming technique
for their solutions. As the cost-to-go functions are convex in these cases, we
use max-affine estimates for their approximations. To train such a max-affine
estimate, we provide a new convex regression algorithm, and evaluate it
empirically for these planning scenarios.
