Decentralized Online Learning Methods Based on Weight-Balancing Over Time-Varying Digraphs

This paper considers decentralized online optimization problems over a graph, where the allocated objective function of each agent is revealed over time and is only known for the corresponding agent in hindsight. Moreover, the graph is directed and time varying. In order to solve the problem, a decentralized stochastic subgradient online learning method is proposed over time-varying digraphs. However, the directed graph could generate an asymmetric weight matrix, which is not doubly stochastic matrix. To overcome this difficulty, we employ a weight-balancing technique. By choosing appropriate learning rates, we show that our proposed method can achieve logarithmic regret under strong convexity. Moreover, under convexity, the square-root regret can also be achieved. In addition, numerical simulations in sensor networks for solving the online distributed estimation problem illustrate the theoretical results.