The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities where each considers contrasting approaches: conditional stochastic optimization frameworks solved using provably optimal structured models versus deep learning models that leverage large data sets to yield empirically effective decision estimators. In this work, we combine the best of both worlds to solve the problem of learning to generate decisions to instances of continuous optimization problems where the feasible set varies with contextual features. We propose a novel framework for training a generative model to estimate optimal decisions by combining interior point methods and adversarial learning which we further embed within an active learning algorithm. Decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Finally, we investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields significant advantages over predict-then-optimize and supervised deep learning techniques, respectively.

翻译：以学习解决优化问题的主题引起了业务研究和机器学习界的注意,其中每个单位都考虑不同的方法:利用可想象的最佳结构模型和深层次学习模型来解决有条件的随机随机优化框架,这些模型利用大数据集产生经验上有效的估计决定者。在这项工作中,我们将两个世界的最佳方法结合起来,以解决学习问题,在可行组合与背景特点不同的连续优化问题中形成决定。我们提议了一个新颖的框架,用于培训一种通过结合内部点方法和对抗性学习来估计最佳决策的基因模型,我们进一步将其纳入积极的学习算法中。我们模型所产生的决定满足了抽样和外抽样的最佳性保证。最后,我们调查组合优化和个性化治疗设计方面的案例研究,表明我们的方法在预测时优化和监督深层学习技术方面分别具有重大优势。