  The presented work addresses two-stage stochastic programs (2SPs), a broadly
applicable model to capture optimization problems subject to uncertain
parameters with adjustable decision variables. In case the adjustable or
second-stage variables contain discrete decisions, the corresponding 2SPs are
known to be NP-complete. The standard approach of forming a single-stage
deterministic equivalent problem can be computationally challenging even for
small instances, as the number of variables and constraints scales with the
number of scenarios. To avoid forming a potentially huge MILP problem, we build
upon an approach of approximating the expected value of the second-stage
problem by a neural network (NN) and encoding the resulting NN into the
first-stage problem. The proposed algorithm alternates between optimizing the
first-stage variables and retraining the NN. We demonstrate the value of our
approach with the example of computing operating points in power systems by
showing that the alternating approach provides improved first-stage decisions
and a tighter approximation between the expected objective and its neural
network approximation.
