Hello, Chiara:
  �Learning by experience.�
  OR
  �Learning from experience.�
    I think that they are both equally �natural�.
  The Oxford English Dictionary gives example sentences:
  �He had learned his lesson by painful experience!�
  �She spoke from experience.�
  Origin: Via Old French from Latin experiential, from expiriri �try�. Compare with Experiment and Expert.
    Oxford Collocations Dictionary.
  Prepositions: by experience; from experience. �We know from experience that hot objects are painful to touch.�
  Verb + experience. Have experience; share experience; learn by experience; learn from experience; �We all learn from experience.� Be based on experience; draw on experience. �In her book, she draws on her first-hand experience of mental illness.� Reflect. �These views reflect my own personal experience.�
  Experience + verb. Suggest something, teach somebody something. �Experience has taught me that life can be very unfair.� �Experience shows that this strategy does not always work.�
    Laurieanne:
  I think that Lynne cunliffe makes a valid point. Whether we accept her choice of �by� or �from� is a matter for discussion.
  However, the fact that experience can have a positive effect, or a negative effect, in my opinion, is not in doubt. Her argument is indirectly supported by the OED words, �try�, and �experiment�.
    You say: I disagree that it means "something has gone wrong".
    However, in the example sentences quoted in these books, the following phrases do suggest that something has gone wrong.
  �Painful experience�; �Painful to touch�; �Mental illness�; �Life can be very unfair�; �Does not always work.�
    Nevertheless, you are right to stress that learning can be a very positive achievement in life.
    In conclusion, I�ll relate a joke that I sometimes tell against myself.
  As you know, I�m a Magician. I stress that I always teach the audience something they didn�t know previously.
  �Ladies and Gentlemen, tonight, you will learn something new. And you will realise that I make my show educational. 
  How do I know that it is educational?
  Because at the end of last night�s performance, I saw a man wake his sleeping wife, and say to her:
  �Well, that�s taught me a Lesson that I�ll not forget in a hurry!� �
   
  Les Douglas