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

In 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 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 gradient-free MXL with callbacks (MXL0
⁺
) algorithm achieves ε-optimality within poly(K, M)/ε
²
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.