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- W2954854410 abstract "In this paper, we quantitative convergence in $W_2$ for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a rate of $tilde{O}lrp{1/sqrt{k}}$ where $k$ is the number of steps; this rate is provably tight up to log factors. Our result reduces to a quantitative form of the classical Central Limit Theorem in the special case when the potential is quadratic." @default.
- W2954854410 created "2019-07-12" @default.
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- W2954854410 date "2019-02-02" @default.
- W2954854410 modified "2023-09-25" @default.
- W2954854410 title "Quantitative Weak Convergence for Discrete Stochastic Processes" @default.
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- W2954854410 doi "https://doi.org/10.48550/arxiv.1902.00832" @default.
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