Learnability and Stability in the General Learning Setting
Shai Shalev-Shwartz, Ohad Shamir, Karthik Sridharan and Nathan Srebro
In: COLT 2009, 18-20 Jun 2009, Montreal.
We establish that stability is necessary and sufficient for learning, even in
the General Learning Setting where uniform convergence conditions are not
necessary for learning, and where learning might only be possible with a
non-ERM learning rule. This goes beyond previous work on the relationship
between stability and learnability, which focused on supervised classification
and regression, where learnability is equivalent to uniform convergence and it
is enough to consider the ERM.