Overfitting in Adaptive Robust Optimization
This addresses stability issues in optimization for decision-making under uncertainty, though it is incremental as it builds on existing ARO frameworks.
The paper tackles the problem of adaptive robust optimization (ARO) policies becoming brittle when uncertainty realizations fall outside the modeled set, analogous to overfitting in machine learning. It proposes assigning constraint-specific uncertainty set sizes as a form of regularization to balance robustness and adaptivity.
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.