Finite-sample guarantees beyond finite candidate sets and independently sampled cost distributions

Extend the finite-sample feasibility and outcome-shortfall guarantees for empirical chance-constrained selection to settings in which cumulative-cost distributions are generated by estimated sequential predictors and strategies range over a parameterized policy class, using an appropriate complexity measure in place of the logarithm of the finite candidate-set size.

Background

The paper proves guarantees for a finite candidate set when each strategy's cost distribution is estimated from independent cost samples. The authors note that an estimated predictor would introduce model error propagated through the sequential dynamics and coupled across stages, while moving from a finite candidate set to a parameterized policy class would require replacing the logarithmic dependence on the candidate-set cardinality with a suitable complexity measure. Both extensions are explicitly deferred.

References

Its error would propagate through the dynamics into the cost tail and be coupled across stages by the sequential structure. They also hold for a finite candidate set. Extending them to a parameterized policy class would therefore require a complexity measure in place of the $\log\lvert\mathcal{G}\rvert$ of Equation~eq:l1const. \citet{rahimian2023contextual} carry a finite-set feasibility bound to a compact decision set along those lines. Both extensions are left to future work.

— Chance-constrained selection of sequential intervention strategies from counterfactual estimates  (2608.13209 - Kim et al., 13 Aug 2026) in Section 3.4, Finite-sample guarantees