针对模型错误设定下的决策风险，提出更稳健的鲁棒贝叶斯模糊集方法。
Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets
- 用鲁棒后验预测分布构建最大均值差异模糊集，应对模型误设问题。
- 在报童与投资组合问题中，外样本表现优于传统贝叶斯与经验DRO方法。
- 适用于数据有限、模型可能错误的高风险决策场景。
分布鲁棒优化（DRO）通过考虑基于经验分布或模型的分布模糊集中的最差情况风险，保护风险厌恶型决策者。为应对有限且含噪数据的影响，基于模型的方法采用贝叶斯框架，将后验不确定性传递至决策问题。然而，当模型存在误设时，决策者需扩大模糊集以包含数据生成过程（DGP），导致决策过于保守。本文提出一种新的方法——鲁棒贝叶斯模糊集分布鲁棒优化（DRO-RoBAS），其使用以鲁棒后验预测分布为中心的最大均值差异（MMD）模糊集，融入对DGP的信念。我们证明该优化问题在再生核希尔伯特空间中存在对偶形式，并给出了模糊集容忍水平的概率保证。在报童（Newsvendor）与投资组合（Portfolio）问题上，多种模型误设情形下，本方法在外样本表现上均优于其他贝叶斯及经验型DRO方法。
原文摘要 · Abstract (English)
Distributionally Robust Optimisation (DRO) protects risk-averse decision-makers by considering the worst-case risk within an ambiguity set of distributions based on the empirical distribution or a model. To further guard against finite, noisy data, model-based approaches admit Bayesian formulations that propagate uncertainty from the posterior to the decision-making problem. However, when the model is misspecified, the decision maker must stretch the ambiguity set to contain the data-generating process (DGP), leading to overly conservative decisions. We address this challenge by introducing DRO with Robust, to model misspecification, Bayesian Ambiguity Sets (DRO-RoBAS). These are Maximum Mean Discrepancy ambiguity sets centred at a robust posterior predictive distribution that incorporates beliefs about the DGP. We show that the resulting optimisation problem obtains a dual formulation in the Reproducing Kernel Hilbert Space and we give probabilistic guarantees on the tolerance level of the ambiguity set. Our method outperforms other Bayesian and empirical DRO approaches in out-of-sample performance on the Newsvendor and Portfolio problems with various cases of model misspecification.
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