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

摘要: 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 based on matrix exponential learning (MXL); and (ii) one-shot gradient estimator which achieves low variance through the reuse of past information. This novel algorithm, call MXL with callbacks (MXL0 $^{+}$ ), retains convergence speed gradient-based methods while requiring minimal feedback per iteration—a single scalar. more detail, channel $K$ users $M$ transmit antennas user, ) algorithm $\varepsilon$ -optimality within ${poly}(K,M)/\varepsilon ^{2}$ iterations (on average high probability), even when implemented fully distributed, asynchronous manner. For cross-validation, also perform series numerical experiments medium- to large-scale networks under realistic conditions. Throughout our experiments, performance MXL0 matches—and sometimes exceeds—that methods, all operating vastly reduced communication overhead. view these findings, appears be uniquely suited distributed massive systems where calculations can become prohibitively expensive.