Stochastic Heavy Ball

Sébastien Gadat (), Fabien Panloup and Sofiane Saadane

No 16-712, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: This paper deals with a natural stochastic optimization procedure derived from the so-called Heavy-ball method differential equation, which was introduced by Polyak in the 1960s with his seminal contribution [Pol64]. The Heavy-ball method is a second-order dynamics that was investigated to minimize convex functions f. The family of second-order methods recently received a large amount of attention, until the famous contribution of Nesterov [Nes83], leading to the explosion of large-scale optimization problems. This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout the iterations of the algorithm. We first describe some almost sure convergence results in the case of general non-convex coercive functions f. We then examine the situation of convex and strongly convex potentials and derive some non-asymptotic results about the stochastic heavy-ball method. We end our study with limit theorems on several rescaled algorithms.

Keywords: Stochastic optimization algorithms; Second-order methods; Random dynamical systems (search for similar items in EconPapers)
Date: 2016-10
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... /2016/wp_tse_712.pdf Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:31104

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().