Optimality of Affine Policies in Multi-stage Robust Optimization

Multistage robust control becomes intractable as the horizon grows, so the field leans on policies that respond affinely to observed disturbances — a practical restriction usually assumed to cost something. For one-dimensional, box-constrained problems with convex state costs and linear control costs, we prove those affine policies are exactly optimal. The argument comes from polyhedral geometry rather than dynamic programming, and yields fast algorithms when the state costs are piecewise affine.

Proceedings of the 48th IEEE Conference on Decision and Control (CDC), pp. 1131–1138