Universal Agent Mixtures and the Geometry of Intelligence

TL;DR

This paper introduces a mathematical framework for combining RL agents through weighted mixtures, revealing geometric properties of agent intelligence and showing that performance measures are essentially environment-dependent averages.

Contribution

It proposes a weighted mixture operation for agents, providing new theorems on the geometry of RL agent intelligence and linking performance measures across environments.

Findings

Weighted mixtures form convex sets of agents.

Symmetries and local extrema in agent intelligence are characterized.

Performance measures are environment-dependent averages.

Abstract

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.