When Robustness Meets Conservativeness: Conformalized Uncertainty Calibration for Balanced Decision Making

2025-10-08

AI Summary

In robust optimization, the robustness level is often set empirically, leading to either insufficient protection or excessive conservatism. While existing data-driven approaches provide finite-sample coverage guarantees, they still require pre-specified coverage targets and lack theoretical guidance for balancing robustness against cost-risk trade-offs. Method: We propose the first distribution-free, finite-sample certifiable robust optimization framework, unifying conformal prediction with robust optimization to construct a Pareto frontier between miscoverage rate and regret upper bound, thereby jointly calibrating robustness and conservatism. Contribution/Results: Our method enables decision-makers to reliably assess and tune robustness levels according to preferences. It significantly improves finite-sample performance on classical optimization problems and delivers interpretable, verifiable robust decision support for high-stakes applications.

Technology Category

Constraint Satisfaction and Optimization: Constraint OptimizationReasoning under Uncertainty: Stochastic OptimizationMachine Learning: Calibration & Uncertainty Quantification

Application Category

User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions. Recent approaches using conformal prediction construct data-driven uncertainty sets with finite-sample coverage guarantees, but they still fix coverage targets a priori and offer little guidance for selecting robustness levels. We propose a new framework that provides distribution-free, finite-sample guarantees on both miscoverage and regret for any family of robust predict-then-optimize policies. Our method constructs valid estimators that trace out the miscoverage-regret Pareto frontier, enabling decision-makers to reliably evaluate and calibrate robustness levels according to their cost-risk preferences. The framework is simple to implement, broadly applicable across classical optimization formulations, and achieves sharper finite-sample performance than existing approaches. These results offer the first principled data-driven methodology for guiding robustness selection and empower practitioners to balance robustness and conservativeness in high-stakes decision-making.

Problem

• Calibrating robustness levels to avoid overly conservative decisions
• Providing finite-sample guarantees for miscoverage and regret simultaneously
• Enabling data-driven selection of optimal robustness-cost tradeoffs

Innovation

• Constructs miscoverage-regret Pareto frontier estimators
• Provides distribution-free finite-sample guarantees
• Enables robust optimization policy calibration