We consider a gossip network, consisting of $n$ nodes, which tracks the information at a source. The source updates its information with a Poisson arrival process and also sends updates to the nodes in the network. The nodes themselves can exchange information among themselves to become as timely as possible. However, the network structure is sparse and irregular, i.e., not every node is connected to every other node in the network, rather, the order of connectivity is low, and varies across different nodes. This asymmetry of the network implies that the nodes in the network do not perform equally in terms of timelines. Due to the gossiping nature of the network, some nodes are able to track the source very timely, whereas, some nodes fall behind versions quite often. In this work, we investigate how the rate-constrained source should distribute its update rate across the network to maintain fairness regarding timeliness, i.e., the overall worst case performance of the network can be minimized. Due to the continuous search space for optimum rate allocation, we formulate this problem as a continuum-armed bandit problem and employ Gaussian process based Bayesian optimization to meet a trade-off between exploration and exploitation sequentially.

翻译：我们考虑一个包含$n$个节点的八卦网络，该网络跟踪信源的信息。信源以泊松到达过程更新其信息，并向网络中的节点发送更新。节点之间可以相互交换信息以尽可能保持时效性。然而，网络结构稀疏且不规则，即并非每个节点都与网络中其他所有节点相连，而是连接度较低且在不同节点间存在差异。这种网络的不对称性意味着网络中节点在时效性表现上并不均衡。由于网络的八卦特性，部分节点能够非常及时地跟踪信源，而另一些节点则经常落后于版本更新。本研究探讨了在速率受限条件下，信源应如何跨网络分配其更新速率以维护时效性方面的公平性，即最小化网络整体的最差性能表现。由于最优速率分配的搜索空间连续，我们将该问题建模为连续臂老虎机问题，并采用基于高斯过程的贝叶斯优化方法，在探索与利用之间实现序贯权衡。