An Ontology-Derived Ground Metric for the Wasserstein Distance Between Pomdp Belief

Introduction. The object of research is the comparison of beliefs obtained from two partially observable Markov decision process (POMDP) models of the same agent using identical action and observation sequences. The components and parameters of these models are represented as individuals in an ontology. Standard divergence calculation methods fail to account for relationships between states when measuring changes in belief. Materials and Methods. An ontology-derived ground metric was defined for the Wasserstein distance between beliefs, combining the path distance between state classes in the hierarchy with the weighted Jaccard distance of their transition and observation probabilities. Three synthetic scenarios were evaluated using an agent based on medical domain of asthma treatment modeling. Each scenario triggers a belief update that transfers the same probability mass to a new state, but with increasing class distance across the three cases. Results. All three scenarios yield a normalised total variation divergence of 0.172. Their normalised Wasserstein divergences are 0.118, 0.152 and 0.169, respectively. The differences arise from the class path term. Conclusions. The class hierarchy allows belief changes to be assessed using relationships between states. This method can be applied to ontology-based decision models where structural changes must be evaluated against both the class hierarchy and the underlying transition and observation dynamics.