It all depends on the situation and the reasons for the aggression. If the aggression is constant for no apparent reason, then this is a fish and you just need to catch it on a mistake. If this is a professional who understands, then doing this can cause you to lose most of the stack without strong enough hands.
re: Poker & Battle for the initiative against aggressor
Against a maniac, this is not a smart battle to pick: You're probably going to lose this fight to be more aggro, and there are much better approaches such as calling him down when you have an above-average hand and letting him spew his stack to you.
Against good players, taking the lead away can be a very good play as you're more likely to win when neither player has much.
Against players who have a "one and done" (cbet and give up) or "bet until raised" strategy
Then making plays to take the initiative (i.e. bluff raising with gutshots) or floating on draw heavy boards so you can apply major pressure when draws complete, has plenty of value.
As Collin said earlier though, against players who are hyper aggressive to the point of being maniacs it's often better to let them hang themselves by slowplaying and trapping. Here's a video that goes a bit more into what I'm talking about.
Remember, when in a hand consider a few things
A) Your Range of Hands & Their Range of Hands
B) The type of opponent you are up against
C) The depth of the stacks
By keeping those in mind before making your decisions you'll have the best chance at picking the best strategic action.
If the aggressor puts money instead of you, then you do not need to think about the size of the bets. There is a positive aspect to this, which can be used wisely. The main thing is that the bet sizes are comfortable for you.
If you don't have a premium hand, it's usually not a good idea. You are violating the rule that you shouldn't inflate pots with bluffs. This is a way of playing that you should never learn. In shorthand no limit games you also have to act more. You can't just wait for good hands like playing longhand. Here it is a good idea to do deceptive 3-bets from time to time. Suitable connectors or small pocket pairs are suitable for deceptive 3-bets. It's like a semi bluff. You get a positive expected value from the fact that your opponent could fold or you win in the showdown. With AA, KK, QQ and AK you can of course always 3-bet for value. But don't battle for the initiative if you only have a medium hand just to have the initiative. That's not a good idea.