## 4 Experiments
### Experimental Results
#### 4.2.2 RQ2: Generality Across Various Communication Conditions and FRSs
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**MovieLens-100K**} & \multicolumn{3}{c}{**MovieLens-1M**} & \multicolumn{3}{c}{**Lastfm-2K**} & \multicolumn{3}{c}{**Foursquare**} \\ \cline{2-13}  & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** & **Round** & **HR** & **NDCG** \\ \hline PFedMF & 243 & 0.7243 & 0.4401 & 231 & 0.7339 & 0.4393 & 243 & 0.8196 & 0.7299 & 238 & 0.8609 & 0.7820 \\ PFedMF-I2 CL & **154** & **0.8409** & **0.6231** & **188** & **0.7937** & **0.5460** & **101** & **0.8332** & **0.7402** & **238** & **0.8627** & **0.7833** \\ \hline PFedGMF & 198 & 0.6448 & 0.3573 & 225 & 0.6521 & 0.3741 & 112 & 0.7935 & 0.7155 & 237 & 0.8571 & 0.7783 \\ PGMF-I2 CL & **179** & **0.8133** & **0.5810** & **136** & **0.7650** & **0.5188** & **89** & **0.8248** & **0.7449** & **138** & **0.8619** & **0.7816** \\ \hline PFedRECON & 247 & 0.7295 & 0.4355 & 297 & 0.7250 & 0.4366 & 198 & 0.8477 & 0.7524 & 166 & **0.8579** & **0.7719** \\ PFedRECON-I2 CL & **146** & **0.8695** & **0.6452** & **256** & **0.8306** & **0.5880** & **47** & **0.8779** & **0.7858** & **116** & 0.8573 & 0.7716 \\ \hline PFedNF & 246 & 0.6871 & 0.3977 & 299 & 0.6945 & 0.4008 & 239 & 0.8154 & 0.7422 & 247 & 0.8507 & 0.7700 \\ PFedNF-I2 CL & **153** & **0.8229** & **0.5995** & **292** & **0.8291** & **0.5882** & **164** & **0.8321** & **0.7538** & **176** & **0.8608** & **0.7843** \\ \hline PFedMLP & 249 & 0.6672 & 0.3849 & 249 & 0.6374 & 0.3622 & 233 & 0.6851 & 0.4806 & 234 & 0.7277 & 0.5130 \\ PFedMLP-I2 CL & **175** & **0.8081** & **0.5834** & **89** & **0.8355** & **0.4721** & **129** & **0.7541** & **0.6320** & **233** & **0.7277** & **0.5143** \\ \hline PFedMAvg & 177 & 0.7169 & 0.4258 & 289 & 0.7264 & 0.4438 & 197 & 0.8080 & 0.7165 & 199 & 0.8687 & 0.6891 \\ PFedMAvg-I2 CL & **62** & **0.8399** & **0.6036** & **169** & **0.8282** & **0.5019** & **83** & **0.8354** & **0.7419** & **158** & **0.8690** & **0.6892** \\ \hline \hline \end{tabular}  
* We have highlighted the superior performance of the FRSs both before and after the implementation of the I2 CL strategy by applying bold formatting.  
\end{table} 
Table 5: Performance of FRSs with or without I2 CL. FRSs introducing I2 CL essentially combine elements of federated training and pure local training. All clients alternate between federated training and pure local training, resulting in a dynamic equilibrium between the two. Federated training contributes to the generalization of item models, whereas pure local training enhances the fit of item models to clients' local data. Over time, as federated training and pure local training achieve dynamic equilibrium, the entire system converges. As in Figures 5c and 6c, the larger the \(p\) or \(r\), the higher the proportion of pure local training in the total number of client training rounds. Higher \(p\) or \(r\) favor pure local training, facilitating rapid convergence and achieving superior performance. In contrast, lower \(p\) or \(r\) favor federated training, resulting in slower convergence but improved generalization capabilities. Figure 5: Learning curves of FedRecI2C with different I2C period \(p\). (**a**) PFedMF-I2 CG. (**b**) FedMF-I2 CG. (**c**) PFedMF-I2 CL. Figure 6: Learning curves of FedRecI2C with different I2C ratio \(r\). (**a**) PFedMF-I2 CG. (**b**) FedMF-I2 CG. (**c**) PFedMF-I2 CL. As shown by the red curves in Figure 5c, when \(p=5\), communication-constrained clients undergo I2 CL every five rounds, and in the following four rounds they may participate in federated training or rest. Each time I2 CL is performed, the system's performance will experience a surge, indicating a shift towards pure local training balance; in training rounds without I2 CL, the learning curves will fall downwards to the balance of federated learning (blue curve); the system finally reaches a dynamic balance between the two.