  For parameterized mixed-binary optimization problems, we construct local
decision rules that prescribe near-optimal courses of action across a set of
parameter values. The decision rules stem from solving risk-adaptive training
problems over classes of continuous, possibly nonlinear mappings. In asymptotic
and nonasymptotic analysis, we establish that the decision rules prescribe
near-optimal decisions locally for the actual problems, without relying on
linearity, convexity, or smoothness. The development also accounts for
practically important aspects such as inexact function evaluations, solution
tolerances in training problems, regularization, and reformulations to
solver-friendly models. The decision rules also furnish a means to carry out
sensitivity and stability analysis for broad classes of parameterized
optimization problems. We develop a decomposition algorithm for solving the
resulting training problems and demonstrate its ability to generate quality
decision rules on a nonlinear binary optimization model from search theory.
