Variance-Reduced Cascade Q-learning: Algorithms and Sample Complexity
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908379456208896 |
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| author | Boveiri, Mohammad Esfahani, Peyman Mohajerin |
| author_facet | Boveiri, Mohammad Esfahani, Peyman Mohajerin |
| contents | We study the problem of estimating the optimal Q-function of $γ$-discounted Markov decision processes (MDPs) under the synchronous setting, where independent samples for all state-action pairs are drawn from a generative model at each iteration. We introduce and analyze a novel model-free algorithm called Variance-Reduced Cascade Q-learning (VRCQ). VRCQ comprises two key building blocks: (i) the established direct variance reduction technique and (ii) our proposed variance reduction scheme, Cascade Q-learning. By leveraging these techniques, VRCQ provides superior guarantees in the $\ell_\infty$-norm compared with the existing model-free stochastic approximation-type algorithms. Specifically, we demonstrate that VRCQ is minimax optimal. Additionally, when the action set is a singleton (so that the Q-learning problem reduces to policy evaluation), it achieves non-asymptotic instance optimality while requiring the minimum number of samples theoretically possible. Our theoretical results and their practical implications are supported by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variance-Reduced Cascade Q-learning: Algorithms and Sample Complexity Boveiri, Mohammad Esfahani, Peyman Mohajerin Machine Learning Systems and Control Optimization and Control We study the problem of estimating the optimal Q-function of $γ$-discounted Markov decision processes (MDPs) under the synchronous setting, where independent samples for all state-action pairs are drawn from a generative model at each iteration. We introduce and analyze a novel model-free algorithm called Variance-Reduced Cascade Q-learning (VRCQ). VRCQ comprises two key building blocks: (i) the established direct variance reduction technique and (ii) our proposed variance reduction scheme, Cascade Q-learning. By leveraging these techniques, VRCQ provides superior guarantees in the $\ell_\infty$-norm compared with the existing model-free stochastic approximation-type algorithms. Specifically, we demonstrate that VRCQ is minimax optimal. Additionally, when the action set is a singleton (so that the Q-learning problem reduces to policy evaluation), it achieves non-asymptotic instance optimality while requiring the minimum number of samples theoretically possible. Our theoretical results and their practical implications are supported by numerical experiments. |
| title | Variance-Reduced Cascade Q-learning: Algorithms and Sample Complexity |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2408.06544 |