Title: Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach Show Chinese title

Title: 使用有限标记数据和训练时间的优化代理 -- 一种半监督贝叶斯神经网络方法

Abstract: Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods. Show Chinese abstract

Abstract: 约束优化问题出现在各种工程系统中，如库存管理和电网。 标准的基于深度神经网络（DNN）的机器学习代理在标记数据稀缺且训练时间有限的实际情况下效果不佳。 我们提出了一种半监督贝叶斯神经网络（BNNs）为基础的优化代理，用于这种复杂情况，其中训练以夹层方式开始，交替进行最小化成本的监督学习步骤和强制约束可行性的一般学习步骤。 我们证明，所提出的半监督BNN在能源网络运行的重要非凸约束优化问题上优于DNN架构，实现了预期最大等式差距的十倍减少，并将不等式差距减半。 此外，BNN提供后验样本的能力被用来在有限的验证数据上构建实际有意义的概率置信区间，这与之前的方法不同。