Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation

2026-03-19

AI Summary

This work addresses the challenge of jointly achieving scenario optimization and conformal prediction with rigorous safety guarantees under limited sample sizes, while appropriately allocating risk across multi-output or multi-stage tasks. From a systems and control perspective, we introduce—for the first time—a natural integration of a sample removal mechanism into the conformal prediction framework, treating discarded samples as acceptable exceptions. We propose a modular risk allocation rule that composes multiple local calibration certificates to construct a unified joint guarantee. The approach leverages exchangeability to derive an average violation law and incorporates multi-step tube-based calibration, making it suitable for multi-output prediction and finite-horizon control. Numerical experiments demonstrate that the proposed strategy effectively balances performance and safety in constraint tightening problems.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationConstraint Satisfaction and Optimization: Constraint OptimizationReasoning under Uncertainty: Stochastic Optimization

Application Category

Security and Privacy: Large-scale security measurementsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Scenario optimization and conformal prediction share a common goal, that is, turning finite samples into safety margins. Yet, different terminology often obscures the connection between their respective guarantees. This paper revisits that connection directly from a systems-and-control viewpoint. Building on the recent conformal/scenario bridge of \citet{OSullivanRomaoMargellos2026}, we extend the forward direction to feasible sample-and-discard scenario algorithms. Specifically, if the final decision is determined by a stable subset of the retained sampled constraints, the classical mean violation law admits a direct exchangeability-based derivation. In this view, discarded samples naturally appear as admissible exceptions. We also introduce a simple modular composition rule that combines several blockwise calibration certificates into a single joint guarantee. This rule proves particularly useful in multi-output prediction and finite-horizon control, where engineers must distribute risk across coordinates, constraints, or prediction steps. Finally, we provide numerical illustrations using a calibrated multi-step tube around an identified predictor. These examples compare alternative stage-wise risk allocations and highlight the resulting performance and safety trade-offs in a standard constraint-tightening problem.

Problem

• Conformal Prediction
• Scenario Optimization
• Discarded Constraints
• Modular Risk Allocation
• Exchangeability

Innovation

• Conformal Prediction
• Scenario Optimization
• Sample-and-Discard
• Modular Risk Allocation
• Exchangeability