The Stochastic Proximal Distance Algorithm

dc.contributor.advisor

Xu, Jason

dc.contributor.author

Jiang, Haoyu

dc.date.accessioned

2023-06-08T18:34:02Z

dc.date.available

2023-06-08T18:34:02Z

dc.date.issued

2023

dc.department

Statistical Science

dc.description.abstract

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and analyze a stochastic version of the recently proposed proximal distance algorithm, a class of iterative optimization methods that recover a desired constrained estimation problem as a penalty parameter $\rho \rightarrow \infty$. By uncovering connections to related stochastic proximal methods and interpreting the penalty parameter as the learning rate, we justify heuristics used in practical manifestations of the proximal distance method, establishing their convergence guarantees for the first time. Moreover, we extend recent theoretical devices to establish finite error bounds and a complete characterization of convergence rates regimes. We validate our analysis via a thorough empirical study, also showing that unsurprisingly, the proposed method outpaces batch versions on popular learning tasks.

dc.identifier.uri

https://hdl.handle.net/10161/27835

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Statistics

dc.title

The Stochastic Proximal Distance Algorithm

dc.type

Master's thesis

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