how to use initializer to set up my multiprocess pool?

The initialize function is called thus:

def worker(...):
    ...
    if initializer is not None:
        initializer(*args)

so there is no return value saved anywhere. You might think this dooms you, but no! Each worker is in a separate process. Thus, you can use an ordinary global variable.

This is not exactly pretty, but it works:

cursor = None
def set_global_cursor(...):
    global cursor
    cursor = ...

Now you can just use cursor in your process_data function. The cursor variable inside each separate process is separate from all the other processes, so they do not step on each other.

(I have no idea whether psycopg2 has a different way to deal with this that does not involve using multiprocessing in the first place; this is meant as a general answer to a general problem with the multiprocessing module.)