Multistep returns, such as n-step returns and λ-returns, are commonly used to improve the sample efficiency of reinforcement learning (RL) methods. The variance of the multistep returns becomes the limiting factor in their length; looking too far into the future increases variance and reverses the benefits of multistep learning. In our work, we demonstrate the ability of compound returns -- weighted averages of n-step returns -- to reduce variance. We prove for the first time that any compound return with the same contraction modulus as a given n-step return has strictly lower variance. We additionally prove that this variance-reduction property improves the finite-sample complexity of temporal-difference learning under linear function approximation. Because general compound returns can be expensive to implement, we introduce two-bootstrap returns which reduce variance while remaining efficient, even when using minibatched experience replay. We conduct experiments showing that compound returns often increase the sample efficiency of n-step deep RL agents like DQN and PPO.
@article{arxiv.2402.03903,
title = {Averaging $n$-step Returns Reduces Variance in Reinforcement Learning},
author = {Brett Daley and Martha White and Marlos C. Machado},
journal= {arXiv preprint arXiv:2402.03903},
year = {2025}
}