TY - GEN
T1 - Probability Maximization with Random Linear Inequalities
T2 - 2018 Annual American Control Conference, ACC 2018
AU - Bardakci, I. E.
AU - Lagoa, C.
AU - Shanbhag, U. V.
N1 - Funding Information:
This research is partially funded by the NSF Grant CNS-1329422 (C. Lagoa) and CMMI-1246887 (CAREER, Shanbhag) U. V. Shanbhag is in the Department of Industrial and Manuf. Engineering, [email protected], while I. E. Bardakci and C. Lagoa are in the Department of Electrical Engineering, the Pennsylvania State University, University Park, PA 16802, USA [email protected]; [email protected].
Publisher Copyright:
© 2018 AACC.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - 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.
AB - 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.
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U2 - 10.23919/ACC.2018.8431483
DO - 10.23919/ACC.2018.8431483
M3 - Conference contribution
AN - SCOPUS:85052584404
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 1396
EP - 1401
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 27 June 2018 through 29 June 2018
ER -