O. Bilenne, P. Mertikopoulos, and E. V. Belmega. In NetGCoop '20: Proceedings of the 2020 International Conference on Network Games, Control and Optimization, 2020.
In wireless communications, the full potential of multiple-input, multiple-output (MIMO) arrays can only be realized through the optimization of their transmission parameters. Distributed solutions dedicated to that end include iterative optimization algorithms involving the computation of the gradient of a given objective function, and its dissemination among the network users. In the context of large-scale MIMO, however, computing and conveying large arrays of function derivatives across a network has a prohibitive cost to communication standards. In this paper we show that multi-user MIMO networks can be optimized without using any derivative information. With focus on the throughput maximization problem in a MIMO multiple access channel, we propose a “derivative-free” optimization methodology relying on very little feedback information: a single function query at each iteration. Our approach integrates two complementary ingredients: exponential learning (a derivative-based expression of the mirror descent algorithm with entropic regularization), and a single-function-query gradient estimation technique derived from a classic approach to derivative-free optimization.