A Discrete-Time Switching System Analysis of Q-learning
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910572248825856 |
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| author | Lee, Donghwan Hu, Jianghai He, Niao |
| author_facet | Lee, Donghwan Hu, Jianghai He, Niao |
| contents | This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time stochastic affine switching system. Moreover, the evolution of the Q-learning estimation error is over- and underestimated by trajectories of two simpler dynamical systems. Based on these two systems, we derive a new finite-time error bound of asynchronous Q-learning when a constant stepsize is used. Our analysis also sheds light on the overestimation phenomenon of Q-learning. We further illustrate and validate the analysis through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08583 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Discrete-Time Switching System Analysis of Q-learning Lee, Donghwan Hu, Jianghai He, Niao Optimization and Control Artificial Intelligence This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time stochastic affine switching system. Moreover, the evolution of the Q-learning estimation error is over- and underestimated by trajectories of two simpler dynamical systems. Based on these two systems, we derive a new finite-time error bound of asynchronous Q-learning when a constant stepsize is used. Our analysis also sheds light on the overestimation phenomenon of Q-learning. We further illustrate and validate the analysis through numerical simulations. |
| title | A Discrete-Time Switching System Analysis of Q-learning |
| topic | Optimization and Control Artificial Intelligence |
| url | https://arxiv.org/abs/2102.08583 |