用后验信息构建不确定性集，提升决策鲁棒性
Distributionally Robust Optimisation with Bayesian Ambiguity Sets
- 基于后验分布定义不确定性集，优化最坏情况风险
- 对指数族模型可推导闭式对偶解，计算高效
- 在报童问题中显著优于传统贝叶斯鲁棒方法
不确定环境下的决策挑战源于数据生成过程（DGP）未知。贝叶斯推断通过参数后验信念估计DGP，但仅最小化后验期望风险可能导致次优决策，尤其在模型不确定性或观测数据有限、噪声大的情况下。为此，本文提出分布鲁棒优化的贝叶斯模糊集方法（DRO-BAS），通过在后验驱动的模糊集中优化最坏情况风险来应对模型不确定性。我们证明该方法对许多指数族分布可获得闭式对偶表示，并在报童问题中展示了其优于现有贝叶斯分布鲁棒方法的样本外稳健性。
原文摘要 · Abstract (English)
Decision making under uncertainty is challenging since the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs about the model's parameters. However, minimising the expected risk under these posterior beliefs can lead to sub-optimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against uncertainty in the model by optimising the worst-case risk over a posterior-informed ambiguity set. We show that our method admits a closed-form dual representation for many exponential family members and showcase its improved out-of-sample robustness against existing Bayesian DRO methodology in the Newsvendor problem.
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