Preferences, risk neutrality and risk-sensitive MDPs
本文证明实数向量空间上满足四个自然公理的二元偏好关系可诱导出一个由线性函数和弱单调函数构成的效用函数，并探讨其对风险敏感折扣马尔可夫决策过程、决策树和经济学中折扣效用模型的重要推论。
Abstract A binary preference relation on a real vector space satisfying four (natural) axioms is shown to induce a utility function composed of a linear function to the reals and a weakly monotonic function. The key axiom is decomposition, and the utility function can be taken to be linear if and only if this axiom’s converse is also satisfied. Important consequences follow for risk-sensitive discounted Markov decision processes, decision trees, and the discounted utility model in economics. Since the four axioms imply that preferences correspond to discounting, the four axioms without the converse imply that preferences are consistent with discounting without risk neutrality.