In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of AC-OPF, and proposes \revision{a novel architecture} that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.

翻译：近年来，基于机器学习的最优潮流优化代理技术引起了广泛关注。尽管在预测高质量原始解方面取得了显著进展，但现有学习方法无法为交流最优潮流（AC-OPF）提供有效的对偶界。本文通过为AC-OPF的凸松弛训练优化代理来填补这一空白。具体而言，本文考虑AC-OPF的二阶锥（SOC）松弛，并提出一种新颖的架构，该架构嵌入快速可微的（对偶）可行性恢复机制，从而提供有效的对偶界。本文将这种新架构与自监督学习方案相结合，避免了昂贵的训练数据生成需求。在中大规模电网上的大量数值实验证明了所提方法的效率和可扩展性。