For those who were in section today, here is why point-by-point maximization works. As discussed in class, maximizing the integral of f(s(x))dx by choosing s(x) is the same as maximizing f(s(x)) by choosing s(x). The concern that was brought up in class was that you might choose an s*( ) that would maximize f for some values of x but not for others. However this would contradict s*( ) being the argmax of f(s(x))! We set no limitations on what s( ) can be - it can be any sort of function at all, piecewise, discontinuous, whatever - and s*( ) is defined as the function s( ) which maximizes f at every point.
The function s*( ) is a rule chosen for every single value of x such that for every single value of x, we have maximized f (and therefore maximized the integral of f with respect to x.)
If you are still confused come grab me.
No comments:
Post a Comment