Integrability Discovery and Agnostic Learning with Unbounded Metric Losses

This manuscript studies distribution-independent agnostic learning with unbounded metric losses on laws having finite best-in-class risk. It relates randomized competitiveness in probability, deterministic almost-sure convergence to global Borel Bayes risk, and discovery of integrable predictors from finite unlabeled sample prefixes. It develops structural results and examples under pointwise-continuous Polish and restricted jointly Borel parametrizations, and distinguishes competitiveness from exact best-in-class convergence. The unrestricted jointly Borel discovery question remains open. No rates or computational guarantees are asserted.