Title: LARO: Learning-Accelerated Two-Stage Adaptive Robust Optimization with Relaxation Guarantees
Primary area: optimization
Keywords: Adaptive Robust Optimization, Two-Phase Decomposition, Machine Learning, Uncertainty Sets, Accelerated Column-and-Constraint Generation

Abstract: Two-stage Adaptive Robust Optimization (ARO) with discrete and polyhedral uncertainty sets incorporates "wait-and-see" decisions to reduce conservatism but remains intractable due to its multi-level structure and mixed-integer recourse. This paper introduces LARO, a learning-accelerated two-phase decomposition framework that scales ARO efficiently without embedding neural networks (NNs) into optimization models. The framework operates in two phases: a Relaxed Master Problem (RMP) that identifies candidate here-and-now decisions through a penalized selection mechanism, where pre-computed severity scores bias scenario choice toward adversarial cases, and a verification phase that ensures restricted worst-case consistency. By decoupling the NN from the RMP, we eliminate solver-compatible embeddings, reduce computational overhead, and enable the use of more expressive neural architectures for recourse evaluation in the adversarial step.  

We establish finite convergence, with the number of iterations bounded by the size of the discrete uncertainty set, and show that the penalized RMP preserves valid lower bound while improving iteration efficiency by prioritizing impactful scenarios. Experiments on robust knapsack and unit commitment problems in power grids demonstrate the scalability of the framework, achieving runtime speedups of up to 10^3 times for knapsack instances and 10^2 times for a 24-bus power network compared to classical column-and-constraint generation. The solve spped is achieved while maintaining optimality gaps typically below 7% for knapsack instances and 2% on the UC problems. This work delivers a severity-aware, learning-accelerated CCG that is both scalable and certifiable, advancing robust decision-making under uncertainty.