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首页> 外文期刊>Information Theory, IEEE Transactions on >Distributed Optimization in an Energy-Constrained Network: Analog Versus Digital Communication Schemes
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Distributed Optimization in an Energy-Constrained Network: Analog Versus Digital Communication Schemes

机译：能量受限网络中的分布式优化：模拟与数字通信方案

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摘要

We consider a distributed optimization problem whereby a network of $n$ nodes, $S_{ell}, ;ell in {1, dots, n}$, wishes to minimize a common strongly convex function $f({bf x}), {bf x}=[x_{1},dots, x_{n}]^{T}$, under the constraint that node $S_{ell}$ controls variable $x_{ell}$ only. The nodes locally update their respective variables and periodically exchange their values with their neighbors over a set of predefined communication channels. Previous studies of this problem have focused mainly on the convergence issue and the analysis of convergence rate. In this study, we consider noisy communication channels and study the impact of communication energy on convergence. In particular, we study the minimum amount of communication energy required for nodes to obtain an $epsilon$-minimizer of $f({bf x})$ in the mean square sense. For linear analog communication schemes, we prove that the communication energy to obtain an $epsilon$ -minimizer of $f({bf x})$ must grow at least at the rate of $Omega (1/epsilon)$, and this bound is tight when $f$ is convex quadratic. Furthermore, we show that the same energy requirement can be reduced to ${cal O} left (log^{2}1/epsilon right)$ if a suitable digital communication scheme is used.
机译：我们考虑一个分布式优化问题，其中$ n $个节点$ S_ {ell}的网络；在{1，点，n} $中的ell希望最小化一个公共的强凸函数$ f（{bf x}），在节点$ S_ {ell} $仅控制变量$ x_ {ell} $的约束下，{bf x} = [x_ {1}，点，x_ {n}] ^ {T} $。节点在本地更新其各自的变量，并通过一组预定义的通信通道定期与邻居交换其值。以前对该问题的研究主要集中在收敛问题和收敛速度分析上。在这项研究中，我们考虑了嘈杂的沟通渠道，并研究了沟通能量对收敛的影响。尤其是，我们研究了节点获得均方根$ f（{bf x}）$的ε-最小化器所需的最小通信能量。对于线性模拟通信方案，我们证明获得$ f（{bf x}）$的$ epsilon $-最小化器的通信能量必须至少以$ Omega（1 / epsilon）$的速率增长，并且当$ f $是二次凸时，它是紧的。此外，我们表明，如果使用合适的数字通信方案，则相同的能量需求可以降低到左{log O}（log ^ {2} 1 /ε右）$。

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