Forgetting-Factor Regret for Distributed Online Optimization

This paper investigates the online distributed optimization problem. First, we propose a novel gradient descent algorithm without a central node under a multi-agent network. Second, the regret with forgetting-factor is introduced. Then the upper bound of the forgetting-factor regret is deduced and sufficient conditions are obtained to guarantee the bounds of the forgetting-factor regret of the algorithm being of the order o(1). Finally, the results are verified through numerical simulation, and the differences between regrets with and without forgetting-factors are compared, which shows that the performance of the forgetting-factors regret is better.