Robust optimization provides a mathematical framework for modeling and
solving decision-making problems under worst-case uncertainty. This work
addresses two-stage robust optimization (2RO) problems (also called adjustable
robust optimization), wherein first-stage and second-stage decisions are made
before and after uncertainty is realized, respectively. This results in a
nested min-max-min optimization problem which is extremely challenging
computationally, especially when the decisions are discrete. We propose
Neur2RO, an efficient machine learning-driven instantiation of
column-and-constraint generation (CCG), a classical iterative algorithm for
2RO. Specifically, we learn to estimate the value function of the second-stage
problem via a novel neural network architecture that is easy to optimize over
by design. Embedding our neural network into CCG yields high-quality solutions
quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital
budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2\%$
of the best-known values in a few seconds compared to the three hours of the
state-of-the-art exact branch-and-price algorithm; for larger and more complex
instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO
outperforms three variants of the $k$-adaptability algorithm, particularly on
the largest instances, with a 5 to 10-fold reduction in solution time. Our code
and data are available at this https URL

该论文研究了两阶段鲁棒优化问题，并提出了一种基于机器学习的方法 Neur2RO 来解决该问题。通过将神经网络嵌入到迭代算法中，Neur2RO 可以高效地找到高质量解决方案。实验证明，与现有算法相比，该方法在几秒内就能找到接近最优解的解决方案。