This paper presents and investigates ARUL, a variant of dynamic belief revision logic in which revision policies, in particular radical, or lexicographic, upgrades, can be arbitrary. We discuss the motivations of having this kind of soft arbitrary operator, concretely for refining the analysis of agentivity and modelling classical epistemic paradoxes. We introduce a sound and complete axiomatic system over models whose accessibility relation is a reflexive, transitive and locally connected preorder, following an approach parallel to Arbitrary Public Announcement Logic (APAL) for proving completeness.