Here is a list of skills that show improvement through 'learn by doing', parsed from my logs.

absorb magic
alloying
amalgamate
analysis of magic lore
attack
avalanche slam
axes
battery
battlecry
blacksmithing
bladed fury
bludgeons
brawling
bypass armour
camping
cardiac stimulation
cast acid
cast destruction
cast generic
cast harm
cast heal
cast information
cast protection
cast rift
cast teleportation
cast transformation
ceremony
chaotic spawn
charge
chest creation
cleave
combat damage analysis
consider
controlled motion
cooking
create armour
create vortex
damage criticality
detect trap
dissection
double mine
double torch
earthquake kick
essence eye
expose weakness
falcon talon strike
falling boulder strike
fire building
first aid
fishing
geyser force kick
hydra fang strike
impale
kick
kiss of death
knowledge of herb conservation
leadership
leather craft
location of weak points
long blades
longbow shot
lure
make reagent
mana control
martial arts
meditation
metal fist
minecrafting
mineral cutting
mining
pin down
plant lore
polearms
pound
power slash
precise slash
protection by sacrifice
quick chant
refining
repair armour
repair item
rift channelling
runic research
seething fervor
shield bash
short blades
skinning
skullsplitter
slash
stab
stalwart stance
study creature
stun
swim
tame mount
tsunami push
vortex analysis
way of the scythe
whips
wound