Ergodicity in reinforcement learning
Abstract
In reinforcement learning, we typically aim to optimize the expected value of the sum of rewards an agent collects over a trajectory. However, if the process generating these rewards is non-ergodic, the expected value, i.e., the average over infinitely many trajectories with a given policy, is uninformative for the average over a single, but infinitely long trajectory. Thus, if we care about how the individual agent performs during deployment, the expected value is not a good optimization objective. In this paper, we discuss the impact of non-ergodic reward processes on reinforcement learning agents through an instructive example, relate the notion of ergodic reward processes to more widely used notions of ergodic Markov chains, and present existing solutions that optimize long-term performance of individual trajectories under non-ergodic reward dynamics.
Cite
@article{arxiv.2603.10895,
title = {Ergodicity in reinforcement learning},
author = {Dominik Baumann and Erfaun Noorani and Arsenii Mustafin and Xinyi Sheng and Bert Verbruggen and Arne Vanhoyweghen and Vincent Ginis and Thomas B. Schön},
journal= {arXiv preprint arXiv:2603.10895},
year = {2026}
}
Comments
Accepted article to appear in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences