Equivalence relations in fully and partially observable Markov decision processes
Pablo Samuel Castro, Prakash Panangaden, Doina Precup · 2009
We explore equivalence relations between states in Markov Decision Processes and Partially Observ-able Markov Decision Processes. We focus on two different equivalence notions: bisimulation [Givan et al., 2003] and a notion of trace equivalence, un-der which states are considered equivalent if they generate the same conditional probability distribu-tions over observation sequences (where the condi-tioning is on action sequences). We show that the relationship between these two equivalence notions changes depending on the amount and nature of the partial observability. We also present an alternate characterization of bisimulation based on trajectory equivalence. 1