This paper considers a game-theoretic framework for distributed machine learning problems over networks where the information acquisition at a node is modeled as a rational choice of a player. In the proposed game, players decide both the learning parameters and the network structure. The Nash equilibrium characterizes the tradeoff between the local performance and the global agreement of the learned classifiers. We first introduce a commutative approach which features a joint learning process that integrates the iterative learning at each node and the network formation. We show that our game is equivalent to a generalized potential game in the setting of undirected networks. We study the convergence of the proposed commutative algorithm, analyze the network structures determined by our game, and show the improvement of the social welfare in comparison with standard distributed learning over fixed networks. To adapt our framework to streaming data, we derive a distributed Kalman filter. A concurrent algorithm based on the online mirror descent algorithm is also introduced for solving for Nash equilibria in a holistic manner. In the case study, we use telemonitoring of Parkinson's disease to corroborate the results.
翻译:本文考虑了网络上分布式机器学习问题的游戏理论框架。 在网络上, 节点上的信息获取模式是一个玩家的合理选择模式。 在提议的游戏中, 玩家决定学习参数和网络结构。 Nash 平衡是当地表现与学习分类者全球协议的权衡的特征。 我们首先引入了一种交流方法, 将每个节点的迭代学习和网络形成结合起来。 我们显示我们的游戏相当于一个无方向网络设置中的普遍潜在游戏。 我们研究拟议的交流算法的趋同, 分析由游戏决定的网络结构, 并显示社会福利的改善, 与固定网络上的标准分配学习相比。 为了调整我们的框架以适应数据流流, 我们从中获取一个分布式的 Kalman 过滤器。 基于在线镜源算法的并行算法也被引入, 以便以整体的方式解决 Nash equilibria 。 在案例研究中, 我们使用 Parkinson 疾病的远程监测来验证结果 。