Risk-Sensitive Planning with One-Switch Utility Functions: Value Iteration
Decision-theoretic planning with nonlinear utility functions is important since decision makers are often risk-sensitive in high-stake planning situations. One-switch utility functions are an important class of nonlinear utility functions that can model decision makers whose decisions change with their wealth level. We study how to maximize the expected utility of a Markov decision problem for a given one-switch utility function, which is difficult since the resulting planning problem is not decomposable. We first study an approach that augments the states of the Markov decision problem with the wealth level. The properties of the resulting infinite Markov decision problem then allow us to generalize the standard risk-neutral version of value iteration from manipulating values to manipulating functions that map wealth levels to values. We use a probabilistic blocks-world example to demonstrate that the resulting risk-sensitive version of value iteration is practical.