If found the expression "to learn to one's cost", which seems to be "learning a lesson at the expense of their money". Some examples:
Thousands of people - mostly internet-savvy men in their 20s or 30s - have learnt to their cost the legal and financial risks involved in file-sharing copyrighted music in large quantities.
Toyota have learnt to their cost that it is far better to be transparent and open when issues are identified than to try and cover up any faults.
Is this an idiom? Another definition of "to learn"?
Would it be correct "to learn to one's health"?