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A STOCHASTIC APPROXIMATION ALGORITHM FOR STOCHASTIC SEMIDEFINITE PROGRAMMING

Published online by Cambridge University Press:  18 May 2016

Bruno Gaujal  and
Panayotis Mertikopoulos
Bruno Gaujal
Affiliation:
Inria and Univ. Grenoble Alpes, LIG F-38000 Grenoble, France E-mail:bruno.gaujal@inria.frhttp://mescal.imag.fr/membres/bruno.gaujal
Panayotis Mertikopoulos
Affiliation:
CNRS (French National Center for Scientific Research), LIG F-38000 Grenoble, France and University Grenoble Alpes, LIG F-38000 Grenoble, France E-mail: panayotis.mertikopoulos@imag.frhttp://mescal.imag.fr/membres/panayotis.mertikopoulos
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Abstract

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Motivated by applications to multi-antenna wireless networks, we propose a distributed and asynchronous algorithm for stochastic semidefinite programming. This algorithm is a stochastic approximation of a continuous-time matrix exponential scheme which is further regularized by the addition of an entropy-like term to the problem's objective function. We show that the resulting algorithm converges almost surely to an ɛ-approximation of the optimal solution requiring only an unbiased estimate of the gradient of the problem's stochastic objective. When applied to throughput maximization in wireless systems, the proposed algorithm retains its convergence properties under a wide array of mobility impediments such as user update asynchronicities, random delays and/or ergodically changing channels. Our theoretical analysis is complemented by extensive numerical simulations, which illustrate the robustness and scalability of the proposed method in realistic network conditions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 3: Erol Gelenbe's 70th Birthday , July 2016 , pp. 431 - 454
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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