打通预测与优化的安全部署路径，实现风险模块化分配。
Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation
- 基于可交换性推导出丢弃样本作为合法例外的理论依据
- 提出模块化组合规则，支持多输出与多步控制的风险分配
- 在多步预测管中验证不同风险分配策略的性能与安全权衡
场景优化与置信预测共享同一目标：将有限样本转化为安全裕度。然而不同术语常掩盖二者保障机制的内在联系。本文从系统与控制视角重新审视这一关联。基于近期工作（OSullivan et al., 2026）建立的置信-场景桥梁，我们将正向映射扩展至保留样本并丢弃约束的可行算法。若最终决策由保留样本中的稳定子集决定，则经典平均违规定律可通过可交换性直接推导。在此框架下，被丢弃样本自然成为可接受的例外。此外，我们提出一种简单模块化组合规则，可将多个局部校准证书合并为单一联合保证。该规则在多输出预测与有限时域控制中尤为有用，工程师需在坐标、约束或预测步间分配风险。最后，我们通过一个经校准的多步预测管对标准约束收紧问题进行数值验证，比较了不同阶段风险分配方案，揭示其性能与安全之间的权衡。
原文摘要 · Abstract (English)
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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