Reinforcement learning with non-ergodic reward increments: robustness via ergodicity transformations
Envisioned application areas for reinforcement learning (RL) include autonomous driving, precision agriculture, and finance, which all require RL agents to make decisions in the real world. A significant challenge hindering the adoption of RL methods in these domains is the non-robustness of conventional algorithms. In particular, the focus of RL is typically on the expected value of the return. The expected value is the average over the statistical ensemble of infinitely many trajectories, which can be uninformative about the performance of the average individual. For instance, when we have a heavy-tailed return distribution, the ensemble average can be dominated by rare extreme events. Consequently, optimizing the expected value can lead to policies that yield exceptionally high returns with a probability that approaches zero but almost surely result in catastrophic outcomes in single long trajectories. In this paper, we develop an algorithm that lets RL agents optimize the long-term performance of individual trajectories. The algorithm enables the agents to learn robust policies, which we show in an instructive example with a heavy-tailed return distribution and standard RL benchmarks. The key element of the algorithm is a transformation that we learn from data. This transformation turns the time series of collected returns into one for whose increments expected value and the average over a long trajectory coincide. Optimizing these increments results in robust policies.