Should you change salt when changing password? Assume a password storage scheme using a computationally-expensive hash algorithm and a CSPRNG salt.  User ID, salt, and hash value are stored in  a table; if the table is compromised, all three values are available to an adversary.

Is there any value in computing a new salt when a user changes his password? 

(I think this question only makes sense if the adversary has before and after copies of the password table, but I could be very wrong about that.)
If the attacker had already begun creating a rainbow table or is engaged in some other attack which requires knowledge of the salt, then a password change with a salt change will require the attacker to start from scratch.

Always assume the attacker has before and after copies of the password hash and salt.

If the salt is not changed, any work the attacker has done may still be applicable to the new password. It may even mean the new password is already in the rainbow table or has been cracked in some other way.