Learning Polyhedral Conformal Sets for Robust Optimization

TL;DR

This paper introduces a decision-aware conformal method for learning polyhedral uncertainty sets tailored to robust optimization, balancing statistical validity with decision-specific performance.

Contribution

It proposes a data-driven, hyperplane-parameterized approach that minimizes robust loss while ensuring finite-sample coverage guarantees and reduced conservatism.

Findings

Provides finite-sample coverage guarantees for the learned sets.

Achieves directional and anisotropic uncertainty modeling aligned with decision objectives.

Demonstrates computational tractability of the proposed method.

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.