L2O-CCG: Adversarial Learning with Set Generalization for Adaptive Robust Optimization

Abstract: The adversarial subproblem in two-stage adaptive robust optimization (ARO), which identifies the worst-case uncertainty realization, is a major computational bottleneck. This difficulty is exacerbated when the recourse value function is non-concave and the uncertainty set shifts across applications. Existing approaches typically exploit specific structural assumptions on the value function or the uncertainty set geometry to reformulate this subproblem, but degrade when these assumptions are violated or the geometry changes at deployment. To address this challenge, we propose L2O-CCG, a bi-level framework that enables the integration of structure-aware adversarial solvers within the constraint-and-column generation (CCG) algorithm. As one instantiation, we develop a generalizable adversarial learning method, which replaces solver-based adversarial search with a learned proximal gradient optimizer that can generalize across uncertainty set geometries without retraining. Here, an inner-level neural network approximates the recourse value function from offline data, while an outer-level pre-trained mapping generates iteration-dependent step sizes for a proximal gradient scheme. We also establish out-of-distribution convergence bounds under uncertainty set parameter shifts, showing how the trajectory deviation of the learned optimizer is bounded by the uncertainty set shift. We illustrate performance of the L2O-CCG method on a building HVAC management task.