Generalizing Diversity with the Signature Transform

Defining differences is a necessary prerequisite for finding diversity in solutions to a given problem. Diversity, in turn, is a property that is difficult to quantify, but is expected to bring favourable properties.We introduce the signature transform as a general behaviour descriptor to distinguish solutions to control problems specifically in the context of Quality-Diversity and MAP-Elites. We define a robustness score and profile, a structured analysis of the behaviour of agents and populations of agents under a changing environment, as an instance of a beneficial property of diversity.The signature transform integrates well with the CVT-Elites approach and offers a functional generalized diversity measure. The robustness analysis substantiates the abstract diversity induced by distance in signature space through tangible effects and enriches the usual evaluation criteria of diverse populations.The generalization of diversity from handcrafted behaviour descriptors opens the possibility to utilise Quality-Diversity techniques for problems where the alignment of the problem with diversity measures is not obvious.