What are your thoughts on training?

If someone at your table chooses to spend their roleplay opportunities and character downtime to undergo rigorous training, should they be rewarded in some way? Would bonus feats / custom trained powers be too strong compared to the other players?

It's basically the way advancement should be done, instead of suddenly learning a new ability out of thin air.

It's a munchkin's dream. It also actively punishes people for choosing to roleplay instead of crunching mechanics via training, because they'll fall behind the people who eschew roleplay for bigger numbers.

I'd only allow it if it was for retraining ie: swapping out feats or bonus attribute points to correct a gimped build.

I always assume characters are honing their skills of screen. If you want to focus on it, cool, you Might get the occasional temporary minor buff. Nothing permanent or super significant.

Lemme run you through a scenario.

Party enters a town and see a scuffle between a master swordsman and bandits. The party swordsman was awestruck at the deft moves and lighting like attacks the swordmaster "flavor" speaking employed. So, in roleplay, he approaches the swordmaster and begs to be taught some of the techniques the swordmaster used.

How would you, ad DM / GM respond?

Make the Swordmaster subplot into a character thing, give him a few trials and such. After a while, if he progresses well in the Swordmaster's eye then you give him a new ability or other way of using his abilities, or even just a cool piece of equipment from his teacher.

I'd talk to the player about it, and figure out what kind of benefit would be appropriate and fit their image of the lessons their character would learn. A lot of it depends on the progression system at play. In Legends of the Wulin, my most commonly played system, I'd likely give them a way to buy into the Heaven Sword Alliance loresheet, which they can invest progression resources in to unlock various transcendent sword techniques.

LotW also offers a neat way of doing short term benefits in the form of Chi Conditions, mechanical bonuses tied to narrative clauses that can have powerful but temporary effects on a characters capabilities.

I think there should always be drawbacks to shit like this. Maybe shit like they're tired and sore for a while from exercise, maybe there's a trade-off in skills, or what have you. A character shouldn't be able to lol-train to get XP

>Maybe shit like they're tired and sore for a while from exercise
Unless they're severely over-training (which any character would notice, so you'd need to warn them of the cut off point where their body can't sustain the exercise) or as out of shape as you are. Most somewhat in shape people can easily train for four to five hours four to five days a week and stay completely in shape. Highly conditioned athletes (which a lot of PCs qualify as) are easily able to go six to eight for six to seven days a week, with the occasional break day.

Isn't that violating both and
when they explain that it shouldn't give them permanent things / punish thise who didn't indulge?

Let's assume that them getting a new power at that point in progression isn't normal.

So like a short term penalty to emphasize their rigorus training, but then they come out with a new technique?