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标题: "Self-Normalized Inference for Constant-Stepsize Temporal-Difference Learning under Markovian Sampling"
原文链接: "https://arxiv.org/abs/2608.10896"
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---

## Statistics > Machine Learning

## Title:Self-Normalized Inference for Constant-Stepsize Temporal-Difference Learning under Markovian Sampling

Authors:[Min Zeng](https://arxiv.org/search/stat?searchtype=author&query=Zeng,+M), [Yichen Zhang](https://arxiv.org/search/stat?searchtype=author&query=Zhang,+Y), [Xiaofeng Shao](https://arxiv.org/search/stat?searchtype=author&query=Shao,+X)

[View PDF](https://arxiv.org/pdf/2608.10896) [HTML (experimental)](https://arxiv.org/html/2608.10896v1)

> Abstract:Constant-stepsize temporal-difference (TD) learning is attractive for policy evaluation, but inference from a single Markov trajectory must account for serial dependence and a stepsize-dependent stationary target. For fixed-stepsize linear TD, we establish a functional central limit theorem whose covariance retains the multiplicative component induced by the random TD matrix and the stationary iterate error. We then derive a joint functional limit for parallel Richardson--Romberg (RR) recursions driven by the same trajectory. A Brownian-bridge self-normalizer yields asymptotically pivotal confidence regions for prespecified state-value contrasts without estimating the long-run covariance or selecting a bandwidth or batch length. For such a contrast, the procedure admits a one-pass implementation whose memory does not grow with the trajectory length. At a fixed stepsize, the inferential center is the RR stationary target. We also study horizon-indexed designs in which the stepsize remains constant within each run and decreases across longer horizons. Under an explicit RR-dependent rate window, the residual RR target shift, multiplicative remainder, and initialization effect are negligible at the root-$n$ scale, yielding inference for the projected Bellman solution. Experiments on FrozenLake and Garnet illustrate stationary-target coverage, RR target correction, and the finite-sample behavior of the horizon-indexed design.

| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| --- | --- |
| Cite as: | [arXiv:2608.10896](https://arxiv.org/abs/2608.10896) \[stat.ML\] |
|  | (or [arXiv:2608.10896v1](https://arxiv.org/abs/2608.10896v1) \[stat.ML\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10896](https://doi.org/10.48550/arXiv.2608.10896) |

## Submission history

From: Min Zeng \[[view email](https://arxiv.org/show-email/e763fae1/2608.10896)\]  
**\[v1\]** Tue, 11 Aug 2026 13:19:28 UTC (148 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10896) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
