Universal Agent Mixtures and the Geometry of Intelligence
This work provides foundational insights into the geometry of intelligence for RL researchers, though it is incremental as it builds on existing multi-agent RL concepts.
The paper introduces a weighted mixture operation for theoretical universal agents in reinforcement learning, showing that the mixture's expected reward in any environment is the weighted average of the original agents' rewards, enabling new theorems about symmetries, convex sets, and local extrema in agent intelligence geometry.
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.