What does a former slave from Tatooine do when his beloved astromech goes missing? He completely ignores the oddly Earth-specific comment from Obi-Wan that ‘astromechs are a dime a dozen‘ (!!!) and heads on out to find him that’s what, and you can see what Anakin does right here in this clip from the season one episode Downfall of a Droid.
After a space chase with General Grievous, Anakin pleads with Obi-Wan that he must find R2-D2 after he goes missing.