Conditions for the Existence of Planning Horizons

Abstract
We consider the general class of discounted problems involving sequential decision making over an unbounded horizon. Under the assumptions of a finite set of policy alternatives at each decision time and costs that are eventually uniformly bounded by some exponential, existence of an optimal infinite horizon strategy is established. Moreover, it is shown that there is a finite horizon version whose first policy decision agrees with an infinite horizon optimal policy. Under the additional assumption that the infinite horizon optimal strategy is eventually cyclic, the stronger result follows that the infinite horizon optimal solution is unique for almost all interest rates and that therefore a planning horizon exists. Algorithmic implications are explored for a restricted subclass of these problems.

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