Learning Polyhedral Conformal Sets for Robust Optimization
cs.LG
Submitted: 2026-05-08
Updated: 2026-09-06
License: http://creativecommons.org/licenses/by/4.0/
The gist: Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set.
Terminology
Abstract
Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.
Sources
- Optimal Model Selection for Conformalized Robust Optimization
- Minimum Volume Conformal Sets for Multivariate Regression
- Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization
- Large-Scale Resilience Planning for Wildfire-Prone Electricity-System via Adaptive Robust Optimization
- End-to-end Conditional Robust Optimization
- Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification
- Valid Selection among Conformal Sets
- Conformal Prediction and Human Decision Making
- Conformal prediction after data-dependent model selection
- Conformal Robust Control of Linear Systems
- Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making
- End-to-End Conformal Calibration for Optimization Under Uncertainty
- Generative Conformal Prediction with Vectorized Non-Conformity Scores
- Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption
- Calibrating Decision Robustness via Inverse Conformal Risk Control
- Conformalized Decision Risk Assessment
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