Robust decisions guaranteed from limited gaussian projection data
Certifying Distributionally Robust Decisions from Projection Observations
Artificial IntelligenceMachine Learning
Summary
This paper addresses how to make reliable decisions when only a single measurement is available, without knowing all the risks involved. The authors study situations where data follows a Gaussian pattern, but the exact details are uncertain. They present a method to identify decisions that remain valid despite this uncertainty, or to admit when a clear choice cannot be made. Their approach includes a way to certify decisions with high confidence and reduces complex risk comparisons to simpler problems. They demonstrate their approach on synthetic tests with error-free outcomes under repeated conditions.
What this means in practice
- •For data analysts: Generate confidence-certified robust decisions from incomplete statistical projections in quality control or risk assessment settings.
- •For financial risk managers: Determine investment decisions that remain sound under uncertain risk measurements using Gaussian-based confidence sets.
Authors
Pouya Ahadi, Kamran Paynabar
Abstract
A scalar measurement can determine a robust decision without identifying the latent covariance or every decision risk. We study finite Gaussian projection experiments with a fixed mean-plus-standard-deviation target. The observation laws define a set of indistinguishable moment models. We exhibit decisions that agree throughout that set despite unidentified risk values, and give a confidence-set certificate that returns a decision or an unresolved outcome. We prove soundness, necessary abstention for indistinguishable models with incompatible optima, and a fixed-checkpoint certification guarantee. A scalar profile reduces nonlinear risk comparisons to convex inner problems. Across seven synthetic instances, jointly calibrated moment regions give sufficient budgets 21 to 52 times explicit expected-sample information lower bounds. Separately measured stopping times are lower, with zero decision errors in 1,900 simulated streams. These comparisons do not constitute matching bounds, and the guarantees require Gaussian replication.