We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including $(f,Γ)$-divergences, we prove a new infimal subadditivity principle showing that, under suitable conditions, a global variational discrepancy is controlled by an average of family-level discrepancies aligned with the graph. In an additive regime, this surrogate is exact. This provides a variational justification for replacing a graph-agnostic GAN with a monolithic discriminator by a graph-informed GAN with localized family-level discriminators. The result does not require the optimizer itself to factorize according to the graph. We also obtain parallel results for integral probability metrics and proximal optimal transport divergences, identify natural discriminator classes for which the theory applies, and present experiments showing improved stability and structural recovery relative to graph-agnostic baselines.

翻译：我们研究当目标分布根据已知贝叶斯网络分解时的对抗学习。对于插值散度（包括$(f,Γ)$-散度），我们证明了一个新的下级次可加性原理，表明在适当条件下，全局变分差异受对齐图结构的家族级差异平均值的控制。在可加性框架下，该替代度量是精确的。这提供了将无图感知GAN（使用单一判别器）替换为图知GAN（使用局部家族级判别器）的变分依据。该结果不需要优化器本身根据图结构分解。我们还在积分概率度量和近端最优传输散度上获得了平行结果，识别了该理论适用的自然判别器类别，并展示了相较于无图感知基线在稳定性和结构恢复方面的改进性实验。