Despite knowing how expensive

[Bassim]

I am wondering if my sentence is grammatically correct. Is it possible to say "regardless" instead of "no matter what"?

Despite knowing how expensive the flight to Australia is, Peter has decided to travel there no matter what.

 

[emsr2d2]

They're both possible but they don't mean the same thing. "regardless" specifically refers to the cost of the flight. "no matter what" means ignoring all other facts/eventualities.