随机时变网络上具有无界次梯度的分布式随机优化
Distributed Stochastic Optimization With Unbounded Subgradients Over Randomly Time-Varying Networks
AI总结：
针对随机时变网络中的分布式优化问题，本文提出带噪声次梯度算法，并在条件平衡与一致条件联合连通条件下证明其几乎必然收敛到全局最优解。
摘要：
受不确定通信网络下分布式统计学习的推动，我们研究了由网络节点执行的分布式随机优化问题，以协作方式最小化凸代价函数之和。网络由一系列时变随机有向图建模，其中每个节点代表一个局部优化器，每条边代表一条通信链路。我们考虑了分布式次梯度优化算法，其中局部代价函数次梯度的测量存在噪声，且每对节点之间的信息交换存在加性和乘性噪声。通过随机李雅普诺夫方法、凸分析、代数图论和鞅收敛理论，我们证明：如果局部次梯度函数线性增长，并且有向图序列是条件平衡且一致条件联合连通的，那么可以设计合适的算法步长，使得所有节点的状态几乎必然收敛到全局最优解。
英文摘要：
Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a communication link. We consider the distributed subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes. By stochastic Lyapunov method, convex analysis, algebraic graph theory and martingale convergence theory, we prove that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
