Game-Theoretic Distributed Empirical Risk Minimization With Strategic Network Design

This article considers a game-theoretic framework for distributed empirical risk minimization (ERM) 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 (NE) characterizes the tradeoff between the local performance and the global agreement of the learned classifiers. We first introduce an interleaved approach that features a joint learning process that integrates the iterative learning at each node with 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 interleaved algorithm, analyze the network structures determined by our game, and show the improvement of social welfare compared to a standard distributed ERM 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 to solve for NE in a holistic manner. In the case study, we use data from telemonitoring of Parkinson's disease to corroborate the results.