Black-Box Assisted Regression: Phase Transitions and Minimax Optimality
Foundation models provide strong but biased priors for downstream tasks with limited labeled data. We formalize black-box assisted nonparametric regression where $\|f^*-f_0\|_{L_2(P_X)}\le\delta$ for unknown $\delta$. We characterize the minimax risk, revealing a phase transition at $\delta_c(n)\asy…