Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift

Minxing Zheng; Holly Wiberg; Shixiang Zhu

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arXiv · 2608.29465

Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift

Minxing Zheng·Holly Wiberg·Shixiang Zhu

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Abstract

Deployed decisions are often optimized once and retained because updates impose operational, regulatory, or switching costs. As operating conditions change, when should such decisions be re-optimized? We study this question for stochastic optimization when the objective's functional form is known but the decision maker's trade-offs are encoded by an unknown preference parameter. Standard distribution-shift tests are poorly aligned with this goal: they can flag detectable yet decision-irrelevant changes without determining whether the incumbent decision has become materially suboptimal. We propose \texttt{RADAR} (Regret-based Assessment of Decision Adequacy and Risk), a decision-focused framework that uses inverse optimization to infer latent preferences and tests the deployed decision's optimality gap under the current distribution. By targeting regret, \texttt{RADAR} ignores decision-irrelevant shifts while detecting changes that warrant re-optimization. We develop two-sample and sequential changepoint procedures and establish asymptotic guarantees for Type-I error and power. Across synthetic optimization problems, a semi-synthetic capacity allocation task, and police-zone planning, \texttt{RADAR} more reliably distinguishes harmful from harmless shifts than decision-agnostic alternatives.

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Minxing Zheng, Holly Wiberg, Shixiang Zhu. 2026-08-29. Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift. https://arxiv.org/abs/2608.29465

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