Operator World Models for Reinforcement Learning

TL;DR

This paper introduces POWR, a reinforcement learning algorithm that uses operator-theoretic world models to enable Policy Mirror Descent, with proven convergence and promising experimental results.

Contribution

It develops a novel world model approach using conditional mean embeddings and operator theory to adapt Policy Mirror Descent for RL.

Findings

Proves convergence rates of POWR to the global optimum.

Demonstrates effectiveness in finite and infinite state environments.

Provides a new framework for model-based RL using operator theory.

Abstract

Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value functions. We address this challenge by introducing a novel approach based on learning a world model of the environment using conditional mean embeddings. Leveraging tools from operator theory we derive a closed-form expression of the action-value function in terms of the world model via simple matrix operations. Combining these estimators with PMD leads to POWR, a new RL algorithm for which we prove convergence rates to the global optimum. Preliminary experiments in finite and infinite state settings support the effectiveness of our method