Averaging $n$-step Returns Reduces Variance in Reinforcement Learning

Brett Daley, Martha White, Marlos C. Machado
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:9904-9930, 2024.

Abstract

Multistep returns, such as $n$-step returns and $\lambda$-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-daley24a, title = {Averaging $n$-step Returns Reduces Variance in Reinforcement Learning}, author = {Daley, Brett and White, Martha and C. Machado, Marlos}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {9904--9930}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/daley24a/daley24a.pdf}, url = {https://proceedings.mlr.press/v235/daley24a.html}, abstract = {Multistep returns, such as $n$-step returns and $\lambda$-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.} }
Endnote
%0 Conference Paper %T Averaging $n$-step Returns Reduces Variance in Reinforcement Learning %A Brett Daley %A Martha White %A Marlos C. Machado %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-daley24a %I PMLR %P 9904--9930 %U https://proceedings.mlr.press/v235/daley24a.html %V 235 %X Multistep returns, such as $n$-step returns and $\lambda$-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.
APA
Daley, B., White, M. & C. Machado, M.. (2024). Averaging $n$-step Returns Reduces Variance in Reinforcement Learning. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:9904-9930 Available from https://proceedings.mlr.press/v235/daley24a.html.

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