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

TL;DR

This work addresses calibrating robustness in predict-then-optimize problems by introducing CREME, an inverse conformal risk-control framework. By fixing uncertainty sets $\mathcal{C}_\lambda(X)$ and certifying both miscoverage and regret across all $\lambda$, CREME constructs valid, distribution-free finite-sample estimates that trace a miscoverage-regret Pareto frontier. The method enables principled, data-driven selection of robustness levels, balancing protection against conservativeness without altering the learning pipeline. Empirically, CREME demonstrates strong validity and accuracy across diverse optimization problems and effectively guides robustness parameter tuning toward near-optimal tradeoffs, offering a practical alternative to ad hoc calibration.

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.

Figures (7)

• Figure 1: A stylized example illustrating the use of our proposed framework. Instead of heuristically fixing a risk level (e.g., $5$%), the decision-maker can use this frontier to select a preferred trade-off. For instance, the curve indicates that reducing risk by up to $25$% (orange dashed line) yields a cost reduction of at least $$150$, corresponding to roughly a $30$% improvement (green dashed line).
• Figure 2: Illustration of the problem setup with a simple robust linear optimization problem. Panel (a) shows the miscoverage-regret tradeoff across three robustness parameters ($\lambda_1, \lambda_2, \lambda_3$). Panel (b) depicts the corresponding robust decisions ($z_1, z_2, z_3$), which differ from the expected optimal decision $z^*$. Panel (c) illustrates an $\ell_\infty$-ball uncertainty set $\mathcal{C}_\lambda$ for the outcome variable $Y$, with the three adversarial outcome vectors ($y_1, y_2, y_3$) labeled. The robustness parameters correspond to the radii of these $\ell_\infty$-norm sets.
• Figure 3: Validity-accuracy tradeoff curves under four optimization settings. Connected dots trace estimator performance as the number of calibration samples $n$ increases from $1$ to $50$, with greater opacity indicating smaller $n$. The proposed method is shown in red, and the baseline Monte Carlo estimator in gray. Both axes represent metrics where higher values indicate better performance ($\uparrow$), so methods appearing closer to the upper-right corner are more desirable.
• Figure 4: Miscoverage–regret tradeoff Pareto frontiers with attained solutions from each model. For a prespecified preference weighting, the black star denotes the true optimal tradeoff. The red dot indicates the tradeoff obtained from the estimated $\hat{\lambda}$ using CREME. Blue markers correspond to three baseline methods that identify $\lambda$ values ensuring the miscoverage rate remains below $5\%$ (vertical dashed blue line).
• Figure 5: An example illustration of a network with three paths considered in our shortest path optimization.

Theorems & Definitions (12)

• Proposition 1
• Theorem 1: Validity
• proof : Proof of \ref{['thm:p-val']}
• Proposition 2: Finite-sample error bound
• Proposition 3: True Pareto frontier
• Corollary 1: Certified Pareto Frontier
• Remark 1
• proof : Proof for \ref{['prop:bound']}
• Corollary 2
• proof : Proof of \ref{['cor:diff-bound']}