  In data-driven optimization, solution feasibility is often ensured through a
"safe" reformulation of the uncertain constraints, such that an obtained
data-driven solution is guaranteed to be feasible for the oracle formulation
with high statistical confidence. Such approaches generally involve an implicit
estimation of the whole feasible set that can scale rapidly with the problem
dimension, in turn leading to over-conservative solutions. In this paper, we
investigate a validation-based strategy to avoid set estimation by exploiting
the intrinsic low dimensionality among all possible solutions output from a
given reformulation. We demonstrate how our obtained solutions satisfy
statistical feasibility guarantees with light dimension dependence, and how
they are asymptotically optimal and thus regarded as the least conservative
with respect to the considered reformulation classes. We apply this strategy to
several data-driven optimization paradigms including (distributionally) robust
optimization, sample average approximation and scenario optimization. Numerical
experiments show encouraging performances of our strategy compared to
established benchmarks.
