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This paper develops new tools to quantify uncertainty in optimal decisionmaking and to gain insight into which variables one should collect informationabout given the potential cost of measuring a large number of variables. Weinvestigate simultaneous inference to determine if a group of variables isrelevant for estimating an optimal decision rule in a high-dimensionalsemiparametric framework. The unknown link function permits flexible modelingof the interactions between the treatment and the covariates, but leads tononconvex estimation in high dimension and imposes significant challenges forinference. We first establish that a local restricted strong convexitycondition holds with high probability and that any feasible local sparsesolution of the estimation problem can achieve the near-oracle estimation errorbound. We further rigorously verify that a wild bootstrap procedure based on adebiased version of the local solution can provide asymptotically honestuniform inference for the effect of a group of variables on optimal decisionmaking. The advantage of honest inference is that it does not require theinitial estimator to achieve perfect model selection and does not require thezero and nonzero effects to be well-separated. We also propose an efficientalgorithm for estimation. Our simulations suggest satisfactory performance. Anexample from a diabetes study illustrates the real application.

Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension