用生成模型提升鲁棒优化，让决策在罕见场景下更稳定。
Generative Distributionally Robust Optimization
- 用采样器与Sinkhorn散度结合，实现无需似然的分布对抗约束。
- 在罕见情境下库存损失降低60%，导航碰撞减少50%。
- 适合需要高鲁棒性的生成式决策系统，如供应链与自动驾驶。
生成模型正被广泛应用于分布鲁棒优化（DRO），但现有方法在模型兼容性与对抗结构间存在权衡：可接受任意采样器的方法不将最差情况分布限制在生成器族内，而参数化生成器的对抗方法则依赖特定模型访问（如似然、得分或训练数据）。我们提出生成式分布鲁棒优化（GDRO），一个原则上统一的框架，能接受任意可采样的条件生成器作为名义模型，并将最差情况分布限制在选定的条件生成器族中。核心是采样器-Sinkhorn配对：采样器精确表示条件分布，而无需似然即可通过样本估计的Sinkhorn散度比较分布。由此得到的总体问题可直接进行有限样本近似，并在活跃决策上下文中实现可微分的原-对偶求解。对于Lipschitz损失，总体Sinkhorn半径可界定下游性能退化。在显式与隐式生成器上，本方法相比名义决策，将罕见情境下的库存遗憾降低60%，社交生成网络（SocialGAN）导航碰撞减少50%。
原文摘要 · Abstract (English)
Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.
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