Eureka! bellman’s principle of optimality is valid!

Abstract

Ever since Bellman formulated his Principle of Optimality in the early 1950s, the Principle has been the subject of considerable criticism. In fact, a number of dynamic programming (DP) scholars quantified specific difficulties with the common interpretation of Bellman’s Principle and proposed constructive remedies. In the case of stochastic processes with a non-denumerable state space, the remedy requires the incorporation of the faithful "with probability one" clause. In this short article we are reminded that if one sticks to Bellman’s original version of the principle, then no such a fix is necessary. We also reiterate the central role that Bellman’s favourite "final state condition" pla..