Postponed linear approximations and adaptive control with non-quadratic losses

Abstract

A new solution approach for stochastic optimal control problems, called postponed linear approximations or PLA, is introduced and applied to MacRae's OLCV adaptive control formulation. Sample calculations are reported demonstrating the accuracy of PLA for computing optimal first period policies. PLA is then used to extend MacRae's formulation to a class of adaptive control problems with non-quadratic, asymmetric loss functions. It is shown that this extension can be quantitatively important, suggesting that misspecification of non-quadratic, asymmetric loss functions by substituting a local or global quadratic approximation may often be a serious error.