用最优传输理论改进风险度量，让智能体在不确定中更安全。
Robust Risk Under Evolving Uncertainty: A Wasserstein Counterpart of the Entropic Value-at-Risk
- 用沃尔什斯坦距离替代相对熵，构建新型鲁棒风险度量
- 能捕捉传统方法忽略的可到达灾难场景，提升安全性
- 动态调整谨慎程度，适合持续学习的智能体决策
一个仍在学习环境的智能体应在无知时谨慎、自信时果断。熵值风险（entropic value-at-risk）通过稳健优化机制实现：置信度决定备选模型的相对熵球半径。但该球无法覆盖名义模型认为不可能的灾难情形，而这正是安全智能体必须对冲的。本文改用最优传输球，研究其诱导的相干风险度量——沃尔什斯坦熵值风险（Wasserstein entropic value-at-risk）。该度量具有类似熵公式的变分对偶形式（逆温度变为运输价格），在风险层级中占据明确位置，并能严格涵盖熵方法所忽视的可达灾难；我们通过数值验证了双重性。将运输半径由信念熵驱动，得到闭式鲁棒动态规划算子，其谨慎程度随信念清晰度上升而收缩，具备认证的安全夹心结构与锐利安全开关。
原文摘要 · Abstract (English)
An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity---a confidence level fixes the radius of a relative-entropy ball of alternative models---but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.
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