Is there any sort of precedent for training to learn / being taught Feats?

I’m interested in acquiring a specific Feat more quickly that just from levelling. It’s a Mastery Feat for the weapon I’ve just portentously received and am proficient with, but would like to become excellent with.

I know that you can gain proficiencies in entire weapons classes as "training", but that’s not quite the same as learning a Feat.

Is there an established process for stuff like this? Naturally, I’m going to talk to my DM about it, but I’m curious to know whether there’s any precedent for it.

Some specifics:

  • Character: Half-Orc Barbarian.
  • Weapon: Spear. (With bonus flavour stuff, but mechanically just a spear most of the time)
  • Feat: Either Polearm Master (errata’d to include Spears) or Spear Mastery (from UA)