Monday, February 13, 2017

Predictive Loss vs. Predictive Regret

It's interesting  to contrast two prediction paradigms.

A.  The universal statistical/econometric approach to prediction:  
Take a stand on a loss function and find/use a predictor that minimizes conditionally expected loss.  Note that this is an absolute standard.  We minimize loss, not some sort of relative loss.

B.  An alternative approach to prediction, common in certain communities/literatures:
Take a stand on a loss function and find/use a predictor that minimizes regret.  Note that this is a relative standard.  Regret minimization is relative loss minimization, i.e., striving to do no worse than others.

Approach A strikes me as natural and appropriate, whereas B strikes me as as quirky and "behavioral".  That is, it seems to me that we generally want tools that perform well, not tools that merely perform no worse than others.

There's also another issue, the ex ante nature of A (standing in the present, conditioning on available information, looking forward) vs. the ex post nature of B (standing in the future, looking backward).  Approach A again seems more natural and appropriate.