Collective Cognition Workshop
Mathematical Foundations of Distributed Intelligence

The goal of the workshop is to explore the current state of research into the mathematical foundations for studies of collectives of self-motivated agents. This field underpins the research and engineering goals of a wide range of disciplines, and includes both research into the behavior of collectives given known micro-scale rules as well as the design of microscale rules to achieve a given system behavior. The ideal endpoint for this workshop would be a concrete program of research on these topics. More realistically, I hope that we can at least agree on a common vocabulary and, perhaps, those features that a theory of collectives must explain. These comments reflect my biases as well as daily, post-workshop discussions.

Any theory of collectives should be able to explain:

• the role of agent diversity and/or noise in establishing the performance level, stability and adaptability of a collective
• the relationship between agent utilities/goals and the performance of the collective as a whole (utility design)
• the relationship(s) between the micro-scale dynamics and the macro-scale dynamics
• how limits on what a system designer can adjust/change/perturb affects the performance levels achievable
• the affects of allowing cooperation between agents

Some important open questions are:

• How can one quantify and disentangle feedback relationships between system levels?
• How can one identify "hidden" variables?
• What "ingredients" are needed to provide a richness of macro-scale behavior or to allow for a particular behavior?
• How can the innovation and the creation of new structures be included?

Large-scale engineering projects can provide important "sanity checks" for any theory. They also are in need of a general theory of collectives in order to make systematic progress and to allow, possibly, the automation of problem decomposition.

One new desideratum for any theory of collectives is that any theory should contain some notion of agent "intelligence" (or maybe fitness?) that is independent from knowledge of the inner workings of the agents. After all, relatively unsophisticated agents can sometimes perform as well or better than quite sophisticated agents as demonstrated in Peter Stone's talk.

Some new questions raised today:

• How can we identify/constuct observables and order parameters for collectives?
• Is the ratio of number of agents to the size of the stategy space always relevant to system performance?

New desiderata: Any theory of collectives should include the role of inter-agent communications and interactions (especially the underlying network structures) in establishing the performance level, stability and adaptability of the collective.

What formalisms are appropriate? Stat. mech., mean field, etc.? Characterization of systems need to account for variances, not just mean behavior...