论文标题
在分布式多用户MIMO系统中使用零订单反馈快速优化
Fast Optimization with Zeroth-Order Feedback in Distributed, Multi-User MIMO Systems
论文作者
论文摘要
在本文中，我们开发了一种无梯度的优化方法，以在高斯MIMO多个访问通道中有效资源分配。我们的方法结合了两种主要成分：（i）基于矩阵指数学习（MXL）的熵半金融优化； （ii）一个单发梯度估计器，通过重复使用过去信息来实现较低的差异。我们称之为带回调的无梯度MXL算法（MXL0 $^{+} $），该小说算法保留了基于梯度的方法的收敛速度，同时需要最小的反馈$ - $ $ - $ $ - $一个单个标量。更详细地，在MIMO多个访问通道中，用$ K $用户和$ m $每个用户传输天线，Mxl0 $^{+} $ algorithm Achieves $ \ text {poly}（p poly}（k，m）/ε^2 $迭代（平均而言），即使在分配的情况下，也可以完全分配，即使在一个完整的情况下，$ \ text {poly}（p poly}（p poly}（k，m）/ε$ - optimality，也是如此。为了进行交叉验证，我们还在现实的通道条件下，在中等至大规模的MIMO网络中进行了一系列数值实验。在我们的整个实验中，MXL0 $^{+} $的性能匹配$ - $，有时超过$ - 基于梯度的MXL方法的$ - $，始终以大大减少的通信开销。鉴于这些发现，MXL0 $^{+} $算法似乎非常适合分布式的大型MIMO系统，在这种分布式上，梯度计算可能会变得非常昂贵。
In this paper, we develop a gradient-free optimization methodology for efficient resource allocation in Gaussian MIMO multiple access channels. Our approach combines two main ingredients: (i) an entropic semidefinite optimization based on matrix exponential learning (MXL); and (ii) a one-shot gradient estimator which achieves low variance through the reuse of past information. This novel algorithm, which we call gradient-free MXL algorithm with callbacks (MXL0$^{+}$), retains the convergence speed of gradient-based methods while requiring minimal feedback per iteration$-$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 $ε$-optimality within $\text{poly}(K,M)/ε^2$ 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.
