  Inspired by recent progress in multi-agent Reinforcement Learning (RL), in
this work we examine the collective intelligent behaviour of theoretical
universal agents by introducing a weighted mixture operation. Given a weighted
set of agents, their weighted mixture is a new agent whose expected total
reward in any environment is the corresponding weighted average of the original
agents' expected total rewards in that environment. Thus, if RL agent
intelligence is quantified in terms of performance across environments, the
weighted mixture's intelligence is the weighted average of the original agents'
intelligences. This operation enables various interesting new theorems that
shed light on the geometry of RL agent intelligence, namely: results about
symmetries, convex agent-sets, and local extrema. We also show that any RL
agent intelligence measure based on average performance across environments,
subject to certain weak technical conditions, is identical (up to a constant
factor) to performance within a single environment dependent on said
intelligence measure.
