@inproceedings{d0b02d34a3f6489b830f528bd5d2e4b7,

title = "On the Information Content of Some Stochastic Algorithms",

abstract = "We formulate an optimization stochastic algorithm convergence theorem, of Solis and Wets type, and we show several instances of its application to concrete algorithms. In this convergence theorem the algorithm is a sequence of random variables and, in order to describe the increasing flow of information associated to this sequence we define a filtration – or flow of σ -algebras – on the probability space, depending on the sequence of random variables and on the function being optimized. We compare the flow of information of two convergent algorithms by comparing the associated filtrations by means of the Cotter distance of σ -algebras. The main result is that two convergent optimization algorithms have the same information content if both their limit minimization functions generate the full σ -algebra of the probability space.",

keywords = "Convergence of information σ -fields, Global optimization, Stochastic algorithms",

author = "Esqu{\'i}vel, {Manuel L.} and N{\'e}lio Machado and Krasii, {Nadezhda P.} and Mota, {Pedro P.}",

note = "Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# Acknowledgements. This work was partially supported, for the first and fourth authors, (Portuguese Foundation for Science and Technology) and, for the third author, through RFBR (Grant n. 19-01-00451). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 5th International Conference on Stochastic Methods, ICSM-5 2020 ; Conference date: 23-11-2020 Through 27-11-2020",

year = "2021",

doi = "10.1007/978-3-030-83266-7_5",

language = "English",

isbn = "978-3-030-83265-0",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "57--75",

editor = "Shiryaev, {Albert N.} and Samouylov, {Konstantin E.} and Kozyrev, {Dmitry V.}",

booktitle = "Recent Developments in Stochastic Methods and Applications - ICSM-5, Selected Contributions",

address = "Netherlands",

}