Interactive decision making: Equivalence of modified formulations

We discuss the use of a quadratic norm for departures from the bliss value of a decision problem under conflicting objectives. The use of a quadratic norm is, for example, of interest within the dynamic framework of optimal control. The symmetric nature of the quadratic norm is relaxed to allow for nonsymmetric preferences. The possibility of tailoring the quadratic objective function to generate optimal policies which are acceptable to the policy maker is explored with two alternative interactive algorithms. One of these is for objective functions with diagonal weighting matrices and uses updates of the bliss values. The second algorithm proceeds by updating non-diagonal weights, while keeping the bliss values fixed. The equivalence of both algorithms is established.