First, Leela only learns from self-play games generated by the client executable you can get from the site. She doesn't doesn't do "live" online learning while playing other opponents.
On the variety thing, yeah, it's tricky because of the way LeelaNice's strength is limited.
The way to get variety with Leela is to use "temperature", which basically tells it to pick moves in proportion to how much they're searched (the way its search works, it ends up searching moves it thinks are better substantially more often than moves it thinks are worse, so it still mostly plays the moves it thinks are best, but occasionally plays suboptimal moves).
The problem is that LeelaNice (unless this has changed recently), importantly relies on doing a single node "search" for limiting strength.
The problem is that temperature doesn't do anything then; since you've only searched a single move, you're going to play that no matter what.
On the other hand, if you increase the number of nodes Leela visits, you can get some variety, but at the "cost" of her becoming much stronger.
There probably is some middle ground that would work decently, like tweaking FPU reduction and pUCT (settings that basically control how much Leela focuses on the moves it thinks are best compared to how much it searches moves it thinks are inferior) and turning on temperature, but that would require a decent bit of tweaking to get right.
Probably worthwhile to investigate, though. I might mention it in the Discord if I remember :)
First, Leela only learns from self-play games generated by the client executable you can get from the site. She doesn't doesn't do "live" online learning while playing other opponents.
On the variety thing, yeah, it's tricky because of the way LeelaNice's strength is limited.
The way to get variety with Leela is to use "temperature", which basically tells it to pick moves in proportion to how much they're searched (the way its search works, it ends up searching moves it thinks are better substantially more often than moves it thinks are worse, so it still mostly plays the moves it thinks are best, but occasionally plays suboptimal moves).
The problem is that LeelaNice (unless this has changed recently), importantly relies on doing a single node "search" for limiting strength.
The problem is that temperature doesn't do anything then; since you've only searched a single move, you're going to play that no matter what.
On the other hand, if you increase the number of nodes Leela visits, you can get some variety, but at the "cost" of her becoming much stronger.
There probably is some middle ground that would work decently, like tweaking FPU reduction and pUCT (settings that basically control how much Leela focuses on the moves it thinks are best compared to how much it searches moves it thinks are inferior) and turning on temperature, but that would require a decent bit of tweaking to get right.
Probably worthwhile to investigate, though. I might mention it in the Discord if I remember :)