Revisiting the Constant Stepsize Stochastic Approximation with Decision-Dependent Markovian Noise
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915937928609792 |
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| author | Hadavi, Hadi Mou, Wenlong Samsonov, Sergey Wai, Hoi-To |
| author_facet | Hadavi, Hadi Mou, Wenlong Samsonov, Sergey Wai, Hoi-To |
| contents | We revisit the convergence analysis of constant stepsize stochastic approximation (SA) with decision-dependent Markovian noise, with a focus on characterizing the stationary bias against the root of the mean-field equation. We first establish the finite-time $p$-th moment bounds for the SA iterates in a general decision-dependent setting, which serve as a stability foundation for the subsequent analysis. Building on this foundation, and leveraging a local regularity condition termed Poisson--Gateaux differentiability (WD$^\ast$) for the solution to Poisson equation induced by the decision-dependent Markov kernel, we show that the stationary bias is of the order $\mathcal{O}(α)$ for a broad class of decision-dependent settings. Additionally, we establish geometric weak convergence of the joint SA process towards a unique stationary distribution, and a functional central limit theorem. Our relaxed regularity condition enables us to cover cases of non-smooth kernels such as acceptance--rejection mechanisms, projected Langevin dynamics, and clipped state dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13378 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisiting the Constant Stepsize Stochastic Approximation with Decision-Dependent Markovian Noise Hadavi, Hadi Mou, Wenlong Samsonov, Sergey Wai, Hoi-To Optimization and Control We revisit the convergence analysis of constant stepsize stochastic approximation (SA) with decision-dependent Markovian noise, with a focus on characterizing the stationary bias against the root of the mean-field equation. We first establish the finite-time $p$-th moment bounds for the SA iterates in a general decision-dependent setting, which serve as a stability foundation for the subsequent analysis. Building on this foundation, and leveraging a local regularity condition termed Poisson--Gateaux differentiability (WD$^\ast$) for the solution to Poisson equation induced by the decision-dependent Markov kernel, we show that the stationary bias is of the order $\mathcal{O}(α)$ for a broad class of decision-dependent settings. Additionally, we establish geometric weak convergence of the joint SA process towards a unique stationary distribution, and a functional central limit theorem. Our relaxed regularity condition enables us to cover cases of non-smooth kernels such as acceptance--rejection mechanisms, projected Langevin dynamics, and clipped state dynamics. |
| title | Revisiting the Constant Stepsize Stochastic Approximation with Decision-Dependent Markovian Noise |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.13378 |