Abstract
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.
Highlights
Semidefinite programming comprises a rich class of convex optimization problems that is both relatively tractable and very powerful
In view of the above, we focus in this paper on stochastic semidefinite programming, a subclass of semidefinite programs where the objective function is given in the form of an expectation with possibly unknown randomness
To assess the performance of (DXL) applied to realistic network conditions, we simulated in Figure 1 a multi-user uplink multiple-input and multiple-output (MIMO) system consisting of a wireless base receiver with 5
Summary
CNRS (French National Center for Scientific Research), LIG F-38000 Grenoble, France and University Grenoble Alpes, LIG F-38000 Grenoble France. 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 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 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
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