Experiments and Additional Results

Note that f(x,c1,c2,) is strongly concave for any (x,c,c) Rd+2.1 2 Impact of the Local Steps: In this section, we run additional experiments to investigate the impact of the local steps K on the training performance. We run FSGDA and SAGDA over the hetergenous "a9a" [40] dataset with the regression model mentioned in Section 4. We fix the local step-size at 0.01, worker number at 100, and choose the number of local update rounds K from the discrete set {2,10,20}. This is due to the fact that the algorithm needs more communication round while K is small, which matches our Corollary 2 and Corollary 3. Impact of the Local Step-size: In this experiment, we choose the value of the local step-sizes from the discrete set {0.0001,0.001,0.01}and As shown in Figure 1(a) and Fig.6(a), larger local step-sizes lead to faster convergence rates. Impact of the Global Step-size: we choose the global step-sizes value from the discrete set {2,5,10} and fix worker number at 100, local update rounds at 10.