Reconciling Universal and Uniform Learning with Q-Aggregation

In bounded regression, minimax excess risk and universal learning have long demanded conflicting algorithmic principles: the former requires improper estimators, while the latter is solved by simple empirical risk minimization. This paper proves that for finite comparator classes, $Q$-aggregation reconciles both worlds by achieving minimax optimal tails alongside universal exponential rates, outperforming alternatives like ERM and star estimation. For countably infinite classes, the authors establish an inherent trade-off between the two criteria, tracing its exact theoretical frontier.