Improving Robust Decisions with Data
Xiaoyu Cheng
TL;DR
This paper investigates how data can improve robust decisions when the data-generating process (DGP) is uncertain and potentially non-identical across experiments. It shows that accommodating the true DGP in data revisions is necessary for objective improvement and identifies monotone and monotone-like decision problems where a truth-accommodating revision guarantees improvement. It then develops practical revision rules, notably the empirical distribution method and the augmented i.i.d. test, with asymptotic and finite-sample guarantees, and demonstrates these methods in parametric applications (Bernoulli with nuisance parameters and Gaussian signals with uncertain variances). The results provide a principled bridge between robustness and learning, offering concrete tools for constructing data-driven revisions that improve outcomes without sacrificing robustness, and clarifying when such improvements are achievable. Overall, the work contributes to robust statistical decisions under non-identical environments by formalizing truth accommodation, proving key sufficiency/impossibility results, and delivering tractable revision procedures with practical relevance.
Abstract
A decision-maker faces uncertainty governed by a data-generating process (DGP), which is only known to belong to a set of sequences of independent but possibly non-identical distributions. A robust decision maximizes the expected payoff against the worst possible DGP in this set. This paper characterizes when and how such robust decisions can be \emph{objectively} improved with data -- that is, yield higher expected payoffs under the true DGP regardless of which DGP is the truth. It further develops simple and novel inference procedures that achieve such improvement, while common methods (e.g., maximum likelihood) may fail to do so.