Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914190384431104 |
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| author | Xu, Yang Ganesh, Swetha Mondal, Washim Uddin Bai, Qinbo Aggarwal, Vaneet |
| author_facet | Xu, Yang Ganesh, Swetha Mondal, Washim Uddin Bai, Qinbo Aggarwal, Vaneet |
| contents | This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $τ_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $τ_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-ε})$ provided that $T \geq \tilde{\mathcal{O}}\left(τ_{\mathrm{mix}}^{2/ε}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm Xu, Yang Ganesh, Swetha Mondal, Washim Uddin Bai, Qinbo Aggarwal, Vaneet Machine Learning Artificial Intelligence This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $τ_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $τ_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-ε})$ provided that $T \geq \tilde{\mathcal{O}}\left(τ_{\mathrm{mix}}^{2/ε}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs. |
| title | Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2505.15138 |