用少量标注数据和短训练时间，实现更可靠的优化代理模型。
Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach
- 采用半监督贝叶斯神经网络，交替进行有监督与无监督学习。
- 在电力系统优化中，等式约束误差降低十倍，不等式约束误差减半。
- 仅需少量验证数据即可生成可信的性能置信区间，适合实际工程部署。
受限优化问题广泛存在于库存管理、电网运行等工程系统中。传统基于深度神经网络（DNN）的代理模型在标注数据稀缺且训练时间受限的实际场景下表现不佳。本文提出一种半监督贝叶斯神经网络（BNN）优化代理方法，训练过程采用夹心式交替策略：先通过有监督学习最小化目标成本，再通过无监督学习保证约束可行性。实验表明，该方法在能源网络运行中的非凸约束优化任务中显著优于标准DNN，使期望最大等式差距降低至原来的十分之一，不等式差距减少一半。此外，利用BNN提供的后验样本，仅需少量验证数据即可构建具有实际意义的性能概率置信区间，优于以往方法。相关代码已开源：https://github.com/kaarthiksundar/BNN-OPF/。
原文摘要 · Abstract (English)
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. The implementation code for this study is available at: https://github.com/kaarthiksundar/BNN-OPF/.
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