Averaging $n$-step Returns Reduces Variance in Reinforcement Learning
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909971280560128 |
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| author | Daley, Brett White, Martha Machado, Marlos C. |
| author_facet | Daley, Brett White, Martha Machado, Marlos C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Averaging $n$-step Returns Reduces Variance in Reinforcement Learning Daley, Brett White, Martha Machado, Marlos C. Machine Learning 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. |
| title | Averaging $n$-step Returns Reduces Variance in Reinforcement Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.03903 |