Parsing boolean values with argparse

I would like to use argparse to parse boolean command-line arguments written as "--foo True" or "--foo False". For example:

my_program --my_boolean_flag False

However, the following test code does not do what I would like:

import argparse
parser = argparse.ArgumentParser(description="My parser")
parser.add_argument("--my_bool", type=bool)
cmd_line = ["--my_bool", "False"]
parsed_args = parser.parse(cmd_line)

Sadly, parsed_args.my_bool evaluates to True. This is the case even when I change cmd_line to be ["--my_bool", ""], which is surprising, since bool("") evalutates to False.

How can I get argparse to parse "False", "F", and their lower-case variants to be False?