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Sharp Structure-Agnostic Minimax Risk for Partial Linear Models

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

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 \(q\in\{μ,π\}\), 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\we

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