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

• URL: http://arxiv.org/abs/2603.19396v1
• Date: Thu, 19 Mar 2026 18:37:58 GMT
• Title: Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation
• Abstract summary: This paper revisits that connection directly from a systems-and-control viewpoint.<n>We introduce a simple modular composition rule that combines several blockwise calibration certificates into a single joint guarantee.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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