Multivariate Utility Optimization with an Application to Risk-Sensitive Partially Observable Markov Decision Processes
Vaios Laschos, Robert J. Seidel, Klaus Obermayer · arXiv (Cornell University) · 2018
We introduce and treat a class of Multi Objective Risk-Sensitive Markov Decision Processes (MORSMDPs), where the optimality criteria are generated by a multivariate function applied on a finite set of \emph{different running costs}. To illustrate our approach, we study the example of a two-armed bandit problem. In the sequel, we show that it is possible to reformulate standard Risk-Sensitive Partially Observable Markov Decision Processes (RSPOMDPs), where risk is modeled by a utility function that is a \emph{sum of exponentials}, as MORSMDPs that can be solved with the methods described in the first part. This way, we extend the treatment of RSPOMDPs with exponential utility to RSPOMDPs corresponding to a qualitatively bigger family of utility functions.