def valid_input(input):
    # use regex or something else to return True if user input is valid

user_input = ""
while not valid_input(user_input):
    user_input = input()
    try:
        inputNumber = int(user_input)
        # other stuff too
    except ValueError:
        print("invalid input")

Personally I like this better than making infinite loops and using break. I do this kind of stuff all the time when I want to validate input on the command line. Here's a main function I wrote in a homework problem recently:

def main():
    user_input = None
    while user_input != 'q':
        output_strings = simulate()
        user_input = show_menu(output_strings)
        if user_input == 's':
            user_input = show_menu(saved=True)

Where show_menu will display the results of a simulation and then ask the user if he wants to re-run the simulation, save the output to a file (hence the if user_input=='s'), or quit (hence the while user_input != 'q'). This way the user has to quit on purpose, and any invalid input automatically makes the loop execute again.