Emergent geometric organization and informative dimensions in coevolutionary algorithms

Coevolutionary algorithms vary entities which can play two or more distinct, interacting roles, with the hope of producing raw material from which a highly-capable composition can be constructed. Ranging in complexity from autodidactic checkers-learning systems to the evolution of competing agents in 3-d simulated physics, applications of these algorithms have proved both motivating and perplexing. Successful applications inspire further application, supporting the belief that a correctly implemented form of evolution by natural selection can produce highly-capable entities with minimal human input or intervention. However, the successes to date have generated limited insight into how to transfer success to other domains. On the other hand, failed applications leave behind a frustratingly opaque trace of misbehavior. In either case, the question of what worked or what went wrong is often left open. One impediment to understanding the dynamics of coevolutionary algorithms is that the interactive domains explored by these algorithms typically lack an explicit objective function. Such a function is a clear guide for judging the progress or regress of an algorithm. However, in the absence of an explicit yardstick to judge the value of coevolving entities, how should they be measured? To begin addressing this question, we start with the observation that in any interaction, an entity is not only performing a task, it is also informing about the capabilities of its interactants. In other words, an interaction can provide a measurement. Entities themselves can therefore be treated as measuring rods, here dubbed informative dimensions, against which other entities are incented to improve. It is argued that when entities are only incented to perform well, and adaptation of the function of measurement is neglected, algorithms tend not to keep informative dimensions and thus fail to produce high-performing entities. It is demonstrated empirically that algorithms which are sensitized to these yardsticks through an informativeness mechanism have better dynamic behavior; in particular, known pathologies such as overspecialization, cycling, or relative overgeneralization are mitigated. We argue that in these cases an emergent geometric organization of the population implicitly maintains informative dimensions, providing a direction to the evolving population and so permitting continued improvement.