סגנון-א-גנוסטי של סכנת-מינימקס-שארפ למודלים-לינאריים-חלקיים

תקציר מקורי באנגליתarXiv:2609.07997v1 Announce Type: new Abstract: We characterize the sharp structure-agnostic minimax risk for coefficient estimation in the partial linear model when the outcome and treatment nuisances are learned by two distinct black-box learners, which resolves the open problem in double machine learning posed by Gu (2025). For each nuisance \(q\in\{\mu,\pi\}\), we characterize the available learner by an approximation-error budget \(a_q\) and a stochastic-error budget \(s_q\), with the latter controlled through localized Rademacher complexity. Writing \(\mathcal E_n\) for the minimax mean-squared error, we show that \[\mathcal E_n\asymp1\wedge\left\{\frac1n+\left(a_\mu a_\pi+\min\left\{a_\pi s_\mu+s_\pi^2,\,a_\mu s_\pi+s_\mu^2\right\}\right)^2\right\}.\] The main new ingredient is a no