通过正则化思想缓解自适应鲁棒优化的过拟合问题
Overfitting in Adaptive Robust Optimization
- 为不同约束分配差异化的不确定性集合大小，强化关键约束
- 紧约束获得更强概率保证，松约束保留灵活性
- 提供可解释的鲁棒性与自适应性权衡设计框架
自适应鲁棒优化（ARO）通过允许决策依赖于实际发生的不确定性，超越了静态鲁棒优化，在建模的不确定性集内弱占优静态解。然而，它使原本与不确定性无关的约束变为依赖关系，当实际值超出不确定性集时，可能导致额外的不可行性。这种自适应策略的脆弱性类似于机器学习中的过拟合。为缓解此问题，我们提出为各约束分配特定的不确定性集合大小，对更严格的约束给予更强的概率保障。从过拟合视角看，这相当于正则化：更紧的保障会收缩自适应系数以确保稳定性，而较松的保障则保留有用灵活性。这一观点推动了一种有原则的不确定性集设计方法，平衡了鲁棒性与自适应性。
原文摘要 · Abstract (English)
Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous constraints that were independent of uncertainty now dependent, making it vulnerable to additional infeasibilities when realizations fall outside the uncertainty set. This phenomenon of adaptive policies being brittle is analogous to overfitting in machine learning. To mitigate against this, we propose assigning constraint-specific uncertainty set sizes, with harder constraints given stronger probabilistic guarantees. Interpreted through the overfitting lens, this acts as regularization: tighter guarantees shrink adaptive coefficients to ensure stability, while looser ones preserve useful flexibility. This view motivates a principled approach to designing uncertainty sets that balances robustness and adaptivity.
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