Learning Theory for Conditional Risk Minimization
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:213-222, 2017.
In this work we study the learnability of stochastic processes with respect to the conditional risk, i.e. the existence of a learning algorithm that improves its next-step performance with the amount of observed data. We introduce a notion of pairwise discrepancy between conditional distributions at different times steps and show how certain properties of these discrepancies can be used to construct a successful learning algorithm. Our main results are two theorems that establish criteria for learnability for many classes of stochastic processes, including all special cases studied previously in the literature.