1. A method of modeling a road characteristic over a region in which a host vehicle is driven, comprising the steps of: operating the host vehicle on roadways having a characteristic that varies over a plurality of predetermined ranges; generating a succession of characteristic values while operating the host vehicle at a predetermined rate, wherein each characteristic value identifies a respective predetermined range then being encountered by the vehicle; updating a Markov chain road-characteristic model stored in an optimizer controller in response to the succession of characteristic values, wherein the model represents respective elements of probability in a matrix of transition events from each predetermined range to a respective next-in-succession range, wherein the optimizer controller stores a current state and a previous state of the matrix; periodically testing a convergence of the current state of the matrix with the previous state of the matrix using KL divergence; if convergence is found then using the current state of the matrix to identify a powertrain control policy optimized for the characterized road characteristic; and adjusting operation of a powertrain of the host vehicle using the identified control policy within a powertrain controller in the host vehicle; wherein each element of the matrix has a value Ï€ i,j representing a weighted frequency of transition events from a first respective characteristic value to a second respective characteristic value divided by a weighted frequency of transition events initiating from the first respective characteristic value, so that the matrix successively approximates the road characteristic of the region.