Probability Maximization with Random Linear Inequalities: Alternative Formulations and Stochastic Approximation Schemes

I. E. Bardakci, C. Lagoa, U. V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper addresses a particular instance of probability maximization problems with random linear inequalities. We consider a novel approach that relies on recent findings in the context of non-Gaussian integrals of positively homogeneous functions. This allows for showing that such a maximization problem can be recast as a convex stochastic optimization problem. While standard stochastic approximation schemes cannot be directly employed, we notice that a modified variant of such schemes is provably convergent and displays optimal rates of convergence. This allows for stating a variable sample-size stochastic approximation (SA) scheme which uses an increasing sample-size of gradients at each step. This scheme is seen to provide accurate solutions at a fraction of the time compared to standard SA schemes.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1396-1401
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Bardakci, I. E., Lagoa, C., & Shanbhag, U. V. (2018). Probability Maximization with Random Linear Inequalities: Alternative Formulations and Stochastic Approximation Schemes. In 2018 Annual American Control Conference, ACC 2018 (pp. 1396-1401). [8431483] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431483