Sequential Decision Processes under Act-State Independence with Arbitrary Choice Functions

Abstract

We investigate how sequential decision processes can be solved, under act-state independence. We first identify a reasonable requirement that such solutions ought to satisfy under act-state independence, which we call locality. We then identify a simple necessary and sufficient algebraic condition on choice functions for locality to be satisfied. As an example, we study locality for some choice functions used in imprecise probability theory, and find that marginal extension plays a crucial role. © Springer-Verlag Berlin Heidelberg 2010.