Certified Decisions
Isaiah Andrews, Jiafeng Chen

TL;DR
This paper introduces a framework for certified decisions that pairs recommended actions with probabilistic inferential guarantees, enabling safer decision-making under uncertainty.
Contribution
It develops a theory of certified decisions using P-certificates and E-certified decisions, linking hypothesis testing to risk-controlled decisions with formal guarantees.
Findings
P-certificates provide probabilistic loss bounds for decisions.
Minimax confidence set-based decisions are optimal for P-certificates.
E-certified decisions extend the framework to unbounded loss scenarios.
Abstract
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with inferential guarantees. Specifically, we attach P-certificates -- upper bounds on loss that hold with probability at least -- to recommended actions. We show that such certificates allow "safe," risk-controlling adoption decisions for ambiguity-averse downstream decision-makers. We further prove that it is without loss to limit attention to P-certificates arising as minimax decisions over confidence sets, or what Manski (2021) terms "as-if decisions with a set estimate." A parallel argument applies to E-certified decisions obtained from e-values in settings with unbounded loss.
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Taxonomy
TopicsRisk and Portfolio Optimization · Decision-Making and Behavioral Economics · Advanced Causal Inference Techniques
MethodsSoftmax · Attention Is All You Need · Sparse Evolutionary Training
