论文标题

用基于能量模型的端到端随机优化

End-to-End Stochastic Optimization with Energy-Based Model

论文作者

Kong, Lingkai, Cui, Jiaming, Zhuang, Yuchen, Feng, Rui, Prakash, B. Aditya, Zhang, Chao

论文摘要

最近提出了以决策为中心的学习(DFL),以解决涉及未知参数的随机优化问题。通过将预测建模与隐式可区分的优化层集成在一起,DFL表现出优于标准的两阶段预测,然后优化管道的性能。但是,大多数现有的DFL方法仅适用于凸问题或一个可以轻松放松到凸的问题的子集。此外,由于需要通过每次训练迭代的优化问题解决和区分培训,因此他们的培训效率效率低下。我们提出了SO-EBM,这是一种使用基于能量的模型的一般有效的DFL方法,用于随机优化。 SO-EBM并没有依靠KKT条件来诱导隐式优化层,而是使用基于能量功能的可区分优化层明确参数化了原始优化问题。为了更好地近似优化景观,我们提出了一个耦合训练目标,该目标使用最大似然损失来捕获最佳位置和基于分配的正规器来捕获整体能量景观。最后,我们根据高斯混合提案提出了具有具有自相应重要性采样器的SO-EBM的有效训练程序。我们在三个应用程序中评估了SO-EBM:功率调度,COVID-19资源分配和非Convex对抗安全游戏,展示了SO-EBM的有效性和效率。

Decision-focused learning (DFL) was recently proposed for stochastic optimization problems that involve unknown parameters. By integrating predictive modeling with an implicitly differentiable optimization layer, DFL has shown superior performance to the standard two-stage predict-then-optimize pipeline. However, most existing DFL methods are only applicable to convex problems or a subset of nonconvex problems that can be easily relaxed to convex ones. Further, they can be inefficient in training due to the requirement of solving and differentiating through the optimization problem in every training iteration. We propose SO-EBM, a general and efficient DFL method for stochastic optimization using energy-based models. Instead of relying on KKT conditions to induce an implicit optimization layer, SO-EBM explicitly parameterizes the original optimization problem using a differentiable optimization layer based on energy functions. To better approximate the optimization landscape, we propose a coupled training objective that uses a maximum likelihood loss to capture the optimum location and a distribution-based regularizer to capture the overall energy landscape. Finally, we propose an efficient training procedure for SO-EBM with a self-normalized importance sampler based on a Gaussian mixture proposal. We evaluate SO-EBM in three applications: power scheduling, COVID-19 resource allocation, and non-convex adversarial security game, demonstrating the effectiveness and efficiency of SO-EBM.

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