Ergodicity in reinforcement learning
This addresses a foundational issue in reinforcement learning for ensuring reliable agent deployment, though it is incremental as it synthesizes and clarifies existing concepts.
The paper tackles the problem that expected value optimization in reinforcement learning is inadequate for non-ergodic reward processes, which can mislead performance for individual agents, and it reviews existing solutions to optimize long-term trajectory performance under such conditions.
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.