scholarly journals A note on continuous-time stochastic approximation in infinite dimensions

2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Jan Seidler ◽  
František Žák
Keyword(s):  
Stochastic Approximation ◽  
Continuous Time ◽  
Infinite Dimensions

scholarly journals A STOCHASTIC APPROXIMATION ALGORITHM FOR STOCHASTIC SEMIDEFINITE PROGRAMMING

2016 ◽  
Vol 30 (3) ◽  
pp. 431-454 ◽  
Author(s):  
Bruno Gaujal ◽  
Panayotis Mertikopoulos
Keyword(s):  
Theoretical Analysis ◽  
Semidefinite Programming ◽  
Stochastic Approximation ◽  
Continuous Time ◽  
Unbiased Estimate ◽  
Optimal Solution ◽  
Wireless Systems ◽  
Throughput Maximization ◽  
Convergence Properties ◽  
Stochastic Semidefinite Programming

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.

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