Forgetting-Factor Regrets for Projection-Free Distributed Online Optimization
Haoran Xu, Zijian Zhu, Shuaiyu Zhou, Yiheng Wei · 2025
This paper introduces the forgetting-factor regret for distributed online optimization to consider the weights of objective functions at different times, which allows the weights of the past objective functions to decay to 0 as the algorithm's running time increases. Most current algorithms have a projection operator, which usually leads to higher computational complexity for high-dimensional problems, in order to solve this problems, a distributed online conditional gradient algorithm with forgetting-factor (DOCGFF) is proposed and its performance under the regret with forgetting factor is analyzed. When the algorithm satisfys some conditions, the bound of our algorithm is of the order$o(1_{/}^{\backslash }$, which means that the regret is independent of the running time$\mathcal{I}$. Finally, a numerical simulation is provided to support the theoretical conclusions.