Overfitting in Adaptive Robust Optimization

Karl Zhu, Dimitris Bertsimas

Keywords: Adaptive Robust Optimization, Overfitting, Regularization, Uncertainty Sets, Probabilistic Guarantees

TL;DR: We show that adaptive robust optimization can overfit its uncertainty set, and propose a regularization perspective with constraint-dependent guarantees to mitigate brittleness.

Abstract: 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.

Submission Number: 111