  Collective intelligence is a fundamental trait shared by several species of
living organisms. It has allowed them to thrive in the diverse environmental
conditions that exist on our planet. From simple organisations in an ant colony
to complex systems in human groups, collective intelligence is vital for
solving complex survival tasks. As is commonly observed, such natural systems
are flexible to changes in their structure. Specifically, they exhibit a high
degree of generalization when the abilities or the total number of agents
changes within a system. We term this phenomenon as Combinatorial
Generalization (CG). CG is a highly desirable trait for autonomous systems as
it can increase their utility and deployability across a wide range of
applications. While recent works addressing specific aspects of CG have shown
impressive results on complex domains, they provide no performance guarantees
when generalizing towards novel situations. In this work, we shed light on the
theoretical underpinnings of CG for cooperative multi-agent systems (MAS).
Specifically, we study generalization bounds under a linear dependence of the
underlying dynamics on the agent capabilities, which can be seen as a
generalization of Successor Features to MAS. We then extend the results first
for Lipschitz and then arbitrary dependence of rewards on team capabilities.
Finally, empirical analysis on various domains using the framework of
multi-agent reinforcement learning highlights important desiderata for
multi-agent algorithms towards ensuring CG.
