Optimality of Affine Policies in Multistage Robust Optimization

Multistage robust optimization is generally intractable, so the field relies on policies that depend affinely on observed disturbances — a restriction adopted for convenience and assumed to be suboptimal. For one-dimensional, constrained problems with convex state costs and linear control costs, we prove affine policies are exactly optimal. The proof turns on the geometry of the feasible set rather than dynamic programming.

Mathematics of Operations Research, vol. 35, no. 2, pp. 363–394