  Empirical risk minimization stands behind most optimization in supervised
machine learning. Under this scheme, labeled data is used to approximate an
expected cost (risk), and a learning algorithm updates model-defining
parameters in search of an empirical risk minimizer, with the aim of thereby
approximately minimizing expected cost. Parameter update is often done by some
sort of gradient descent. In this paper, we introduce a learning algorithm to
construct models for real analytic functions using neither gradient descent nor
empirical risk minimization. Observing that such functions are defined by local
information, we situate familiar Taylor approximation methods in the context of
sampling data from a distribution, and prove a nonuniform learning result.
