Assume you have a game tree and the features $(f_1, f_2, f_3,\ldots,f_n )$ that describe the state of the game at any node. Also assume that you are using depth-limited minimax and always expand up to a fixed depth d. Say you have the following four evaluation functions:
$F_1=w_1f_1+w_2f_2+\cdots+f_n$.
$F_2=w_1f_1^2+w_2f_2^2+\cdots+f_n^2$.
$F_3=\exp(w_1f_1^2+w_2f_2^2+\cdots+f_n^2)$.
$F_4=w_1f_1f_2+w_2f_2f_3+⋯+w_nf_{n-1}f_n$.
The weights $(w_1,w_2,\ldots,w_n)$ are same for all evaluation functions. Then select all the statements that are correct:
The optimal sequence of moves for the MAX player would be the different for the function $F_1$ and $F_2$.
The optimal sequence of moves for the MAX player would be the different for the function $F_2$ and $F_3$
The optimal sequence of moves for the MAX player would be the different for the function $F_1$ and $F_3$
The optimal sequence of moves for the MAX player would be necessarily the same for all the functions
None of the above are correct
I need help with this problem that I came across. My understanding on this is that unless weights are changed the evaluation function should be the same. that is, in this case statement 2 and 3 are the only ones correct.
Any ideas?
