Good question. Because after a while all asteroids are completely depleted and if you haven't researched the "better mining" techs much sooner than it may be a complete waste of money/resources to do it afterwards.
Actually, Since the techs only make you mine faster, not more (total amount of mins per asteroid is still the same) I think its better to wait till all your asteroids are depleted, then research the minerals, as spending minerals so you can deplete your suply faster seems counterintuitive. But I guess it all depends on how soon you need the minerals, if you need more in the beginning, or later in the game, I guess it would end up being the same thing.
I don't think it is a waste of money to get it after your asteroids are depleted if it gives a bonus, as a depleted asteroid will stay mining at the same rate. But what I'm basically saying is that it really is the same thing to get the techs at the beginning of the game (asap) as getting it as soon as all your asteroids are depleted, but once your asteroids are depleted, I think every second is a fraction more of minerals wasted.