Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916197161762816 |
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| author | Lee, Donghwan |
| author_facet | Lee, Donghwan |
| contents | This paper analyzes multi-step TD-learning algorithms within the `deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, and the control theoretic approach, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation Lee, Donghwan Systems and Control Machine Learning This paper analyzes multi-step TD-learning algorithms within the `deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, and the control theoretic approach, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms. |
| title | Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2402.15781 |