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Quantitative Weak Convergence for Discrete Stochastic Processes
- Publication Year :
- 2019
-
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.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1902.00832
- Document Type :
- Working Paper