Fast Optimization with Zeroth-Order Feedback in Distributed, Multi-User MIMO Systems

International audienceIn this paper, we develop a gradient-free optimization methodology for efficient resource allocation in Gaussian MIMO multiple access channels. Our approach combines two main ingredients: (i) an entropic semidefinite optimization based on matrix exponential learning (MXL); and (ii) a one-shot gradient estimator which achieves low variance through the reuse of past information. This novel algorithm, which we call gradient-free MXL algorithm with callbacks (MXL0+), retains the convergence speed of gradient-based methods while requiring minimal feedback per iteration−a single scalar. In more detail, in a MIMO multiple access channel with K users and M transmit antennas per user, the MXL0+ algorithm achieves ϵ-optimality within poly(K,M)/ϵ2 iterations (on average and with high probability), even when implemented in a fully distributed, asynchronous manner. For cross-validation, we also perform a series of numerical experiments in medium- to large-scale MIMO networks under realistic channel conditions. Throughout our experiments, the performance of MXL0+ matches−and sometimes exceeds−that of gradient-based MXL methods, all the while operating with a vastly reduced communication overhead. In view of these findings, the MXL0+ algorithm appears to be uniquely suited for distributed massive MIMO systems where gradient calculations can become prohibitively expensive