风险敏感部分可观测马尔可夫决策过程作为完全可观测多变量效用最优化问题
Risk-Sensitive Partially Observable Markov Decision Processes as Fully Observable Multivariate Utility Optimization problems
摘要：
当风险由一个效用函数建模，且状态空间和观测空间都是有限的时，我们给出了一个求解风险敏感部分可观测马尔可夫决策过程的新算法.该算法是基于这样的观察，即用于指数效用函数的测量的改变和随后的信息空间的引入实际上可以扩展为指数的和，如果引入跟踪对应于每个指数的“预期累积成本”的额外的向量参数。由于每一个增函数都可以用有限区间内的指数和来近似，因此该方法基本上可以应用于任何效用函数，其复杂性取决于指数的数量。
英文摘要：
We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based on an observation that the change of measure and the subsequent introduction of the information space that is used for exponential utility functions, can be actually extended for sums of exponentials if one introduces an extra vector parameter that tracks the "expected accumulated cost" that corresponds to each exponential. Since every increasing function can be approximated by sums of exponentials in finite intervals, the method can be essentially applied for any utility function, with its complexity depending on the number of exponentials.
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