演化不确定性下的鲁棒风险：熵值风险（Entropic Value-at-Risk）的Wasserstein对应
Robust Risk Under Evolving Uncertainty: A Wasserstein Counterpart of the Entropic Value-at-Risk
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中文总结 AI 辅助
该研究针对演化不确定性下的鲁棒风险问题，提出Wasserstein熵值风险，弥补熵值风险无法对冲名义模型认定不可能的灾难的缺陷，经数值验证其变分对偶性，并构造出随信念变化的闭式鲁棒动态规划算子。
中文摘要 AI 辅助
仍在学习环境的智能体应在无知时谨慎，自信时大胆。熵值风险（Entropic Value-at-Risk）通过鲁棒优化恒等式实现这一点——置信水平确定替代模型的相对熵球半径——但该球无法触及名义模型认为不可能的灾难，而这正是安全智能体必须对冲的。我们转而使用最优运输球，研究其诱导的相干风险测度Wasserstein熵值风险。它具有镜像熵公式的变分对偶（逆温度变为运输价格），在风险层级中占据确定位置，且可证明能解释熵测度忽略的可及灾难；我们通过数值验证两种对偶性。将运输半径由信念熵驱动，得到闭式鲁棒动态规划算子，其谨慎性随信念尖锐化而收缩，具备经证明的安全区间和清晰的安全切换机制。
英文摘要
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.
发表机构
- Technical University of Munich（慕尼黑工业大学）
- Masaryk University（马萨里克大学）
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