Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation
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| Format: | Preprint |
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2026
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| _version_ | 1866917354050420736 |
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| author | Calafiore, Giuseppe C. |
| author_facet | Calafiore, Giuseppe C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_19396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation Calafiore, Giuseppe C. Systems and Control Machine Learning 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. |
| title | Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2603.19396 |