Online Federated Reproduced Gradient Descent With Time-Varying Global Optima

This paper addresses an online federated learning problem, where the time drift in data distribution leads to time-varying global optima. To adapt to the drift, this paper designs a random Fourier features (RFF) model combined with Reproducing Kernel Hilbert Space (RKHS) theory to tracking the global gradient. Meanwhile, the model also can mitigate gradient variance from local data and gradient bias due to data heterogeneity. Based on this model, the paper further proposes an online federated reproduced gradient descent (OFedRGD) algorithm. The Wasserstein distance is then employed as a distribution metric to analyze the regret by OFedRGD, which is composed of cumulative distribution drifts and cumulative gradient error caused by stochasticity and heterogeneity. Additionally, a set of CLEAR-datasets, including two online learning tasks, are used to test the proposed algorithm. The results show that the proposed algorithm can effectively improve classification accuracy in the two tasks by $5\%$ and $16\%$, respectively, and its performance is less adversely affected by the degree of data dispersion.