Reconciling Universal and Uniform Learning with $Q$-Aggregation
Read the original on arXiv Statistics ML →The paper investigates regression with bounded responses, comparing two learning frameworks: model selection aggregation, which requires improper algorithms to achieve minimax excess risk, and universal learning, where empirical risk minimization suffices for exponential learning rates. For finite hypothesis classes, the authors show that the $Q$-aggregation estimator simultaneously attains minimax optimal tails and exponential universal rates, while other common estimators fail to do so. For countably infinite classes, they prove an inherent trade‑off between exponential universal and minimax uniform rates, resolved by combining optimal algorithms from each framework via $Q$-aggregation.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.