2023
DOI: 10.48550/arxiv.2302.07690
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Online Statistical Inference for Nonlinear Stochastic Approximation with Markovian Data

Abstract: We study the statistical inference of nonlinear stochastic approximation algorithms utilizing a single trajectory of Markovian data. Our methodology has practical applications in various scenarios, such as Stochastic Gradient Descent (SGD) on autoregressive data and asynchronous Q-Learning. By utilizing the standard stochastic approximation (SA) framework to estimate the target parameter, we establish a functional central limit theorem for its partial-sum process, φ T . To further support this theory, we provi… Show more

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“…To extend the applicability of our work to more general settings, it would be valuable to explore weaker assumptions. Li et al (2023) and Liu et al (2023) have considered Markovian data and ϕ-mixing data for convex SGD, respectively. Adapting our analysis to these more general situations holds great potential.…”
Section: Discussionmentioning
confidence: 99%
“…To extend the applicability of our work to more general settings, it would be valuable to explore weaker assumptions. Li et al (2023) and Liu et al (2023) have considered Markovian data and ϕ-mixing data for convex SGD, respectively. Adapting our analysis to these more general situations holds great potential.…”
Section: Discussionmentioning
confidence: 99%