Dynamic programming and principles of optimality

A sequential decision model is developed in the context of which three principles of optimality are defined. Each of the principles is shown to be valid for a wide class of stochastic sequential decision problems. The relationship between the principles and the functional equations of dynamic programming is investigated and it is shown that the validity of each of them guarantees the optimality of the dynamic programming solutions. As no monotonicity assumption is made regarding the reward functions, the results presented in this paper resolve certain questions raised in the literature as to the relation among the principles of optimality and the optimality of the dynamic programming solutions.