An Informal Look at the Principle of Optimality

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Abstract
The Principle of Optimality is examined informally in the context of discounted Markov decision processes. Our purpose is to illustrate that one should be invoking the optimality equations and/or the optimality criterion, rather than the Principle of Optimality in analyzing dynamic models. A counterexample to one interpretation of the Principle is given. It involves a foolish action at the second stage from a state that can be reached, but with probability zero. Redefining optimality as in Hinderer [Hinderer, K. 1970. Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter. Springer-Verlag, New York.], restores the Principle, at the cost of a weaker notion of optimality.

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