[J15] - A stochastic approximation algorithm for stochastic semidefinite programming

B. Gaujal and P. Mertikopoulos. Probability in the Engineering and Informational Sciences, vol. 30, no. 3, pp. 431-454, July 2016.


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 continous- time matrix exponential scheme regularized by the addition of an entropy-like term to the problem’s objective function. We show that the resulting algo- rithm converges almost surely to an ε-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 multiple- input and multiple-output (MIMO) 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.

arXiv link: https://arxiv.org/abs/1507.01859

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