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

TL;DR

This paper introduces a gradient-free optimization algorithm for resource allocation in distributed MIMO systems, achieving fast convergence with minimal feedback and reduced communication overhead, suitable for large-scale networks.

Contribution

The paper presents MXL0$^{+}$, a novel gradient-free, entropic semidefinite optimization algorithm that converges efficiently in distributed MIMO systems with minimal feedback.

Findings

MXL0$^{+}$ achieves $ ext{poly}(K,M)/ ext{epsilon}^2$ convergence rate.

The algorithm performs comparably or better than gradient-based methods in simulations.

It requires only a single scalar feedback per iteration, reducing communication overhead.

Abstract

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 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 $\epsilon$-optimality within $\text{poly}(K,M)/\epsilon^2$ 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.