A General Characterization of Universal Exponential Squared-Loss Learning

This manuscript studies universal exponential agnostic squared-loss learning for jointly Borel-parametrized classes of [0,1]-valued functions on standard Borel domains. It characterizes the learning property by scatteredness of the full pointwise closure and a local condition fixing strictly interior-valued coordinates. The upper bound uses a universally measurable improper learner and distribution-dependent exponential probabilities for positive excess risk, without requiring attainment of the comparator infimum. The work does not assert computational efficiency, jointly Borel learnability, or a classification of slower rates.