Say I have two algorithms to choose from. Both give the same result, but I want to pick the one which has the lowest cost (could be computational or other). For purposes of simplification, assume that both algorithms return a result from 0 to 100. One algorithm, "Algorithm A" is more efficient for all results from 0 to under 50 and the other one, "Algorithm B", is more efficient for all results over 50 to 100. Both are equally efficient at 50. Then my cost or penalty function might look something like this:
Algorithm A: 0 if under 50, else c(x) = 2*(x - 50) if above 50 Algorithm B: 0 if over 50, else c(x) = 1.3*(50 - x) if below 50
Where x is the result of the algorithm and I seek to minimize the cost, c. Given the asymmetrical classification penalty, how would I adjust my prediction of x? Qualitatively, I would want to bias my prediction towards the algorithm with the lower cost function. Example, if my guess is exactly 50, I'd choose algorithm B due to the lower cost function in case I'm wrong. But how do I model this mathematically? I think the answer will depend on the variance or accuracy of how well I can predict x.