On Gaussian approximation for entropy-regularized Q-learning with function approximation
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913137413849088 |
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| author | Rubtsov, Artemy Singh, Rahul Moulines, Eric Naumov, Alexey Samsonov, Sergey |
| author_facet | Rubtsov, Artemy Singh, Rahul Moulines, Eric Naumov, Alexey Samsonov, Sergey |
| contents | In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial stepsize $k^{-ω}$, $ω\in (1/2,1)$. Assuming that the sequence of observed triples $(s_k,a_k,s_{k+1})_{k \geq 0}$ forms a uniformly geometrically ergodic Markov chain, and under suitable regularity conditions for the projected soft Bellman equation, we establish a Gaussian approximation bound in the convex distance with rate of order $n^{-1/4}$, up to polylogarithmic factors in $n$, where $n$ is the number of samples used by the algorithm. To obtain this result, we combine a linearization of the soft Bellman recursion with a Gaussian approximation for the leading martingale term. Finally, we derive high-order moment bounds for the algorithm's last iterate, which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Gaussian approximation for entropy-regularized Q-learning with function approximation Rubtsov, Artemy Singh, Rahul Moulines, Eric Naumov, Alexey Samsonov, Sergey Machine Learning In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial stepsize $k^{-ω}$, $ω\in (1/2,1)$. Assuming that the sequence of observed triples $(s_k,a_k,s_{k+1})_{k \geq 0}$ forms a uniformly geometrically ergodic Markov chain, and under suitable regularity conditions for the projected soft Bellman equation, we establish a Gaussian approximation bound in the convex distance with rate of order $n^{-1/4}$, up to polylogarithmic factors in $n$, where $n$ is the number of samples used by the algorithm. To obtain this result, we combine a linearization of the soft Bellman recursion with a Gaussian approximation for the leading martingale term. Finally, we derive high-order moment bounds for the algorithm's last iterate, which might be of independent interest. |
| title | On Gaussian approximation for entropy-regularized Q-learning with function approximation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.17678 |