Affine Structure and Invariant Policies for Dynamic Programs

This paper studies a family of sequential decision processes whose affine structure is shown to imply that attention can be restricted to policies that select the same decision for all states. A sequence of n invariant policies (decisions) is shown to be optimal when the planning horizon is n epochs. When the planning horizon is infinite, added structure is imposed, and a stationary invariant policy is shown to be optimal. Computational methods and examples are included.