Learnability and Stability in the General Learning Setting
Shai Shalev-Shwartz, Ohad Shamir, Nathan Srebro and Karthik Sridharan
In: COLT 2009(2009).

Abstract

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.

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