# QoE Modeling on Split Features with Distributed Deep Learning
## 6 Results
### Optimizing \(vFL\) Training: Data Volume and Training Time Perspectives  
We present results from the network footprint of the \(vFL\) and make comparisons on different hyper-parameters. In these experiments, we set the split index to 4. We tuned the \(vFL\) training to optimize (decrease training time, and exchanged data volume among the nodes) while sustaining the test set's F1-score performance. Originally, the average data size that was transmitted was 90 KB. We used a combination of the following approaches: reducing the number of neurons (from 32 to 8) in the cut-layers of the nodes, applying Eliasgamma [27] coding on the transmitted data and finally, compressing it further with the lz4 code via pyarrow [28]. As the training process is iterative, the expected size of the data being transmitted is proportional to the number of iterations. The latter depends on how fast the model accuracy converges to an acceptable level over the rounds. A convergence criterion can be set based on similar SOTA (state-of-the-art) techniques [40], as such when an accuracy level that does not increase at all within the last rounds. Aside from the privacy preserving properties, the solution is even more appealing when the partitioned model sizes and/or the training datasets used on those local nodes are very large with very high network footprint when transferred in between if _Fully Centralized_ would have been an option. Therefore, to further improve the network footprint and the training time to potentially yield more energy-efficient \(vFL\), we perform a few more experiments. These experiments involve adjusting the neuron size at the cut-layer of the \(vFL\) architecture. Table 3 reveals the impact of the Elias encoding on the network footprint (in terms of the average number of bytes per transmission) and the training times. The results are obtained when all scenarios are trained with 4000 rounds. Obviously, this encoding yields a significant reduction (average 25%) of the amounts of data to be sent across the network, which has to come partly at the expense of increased training time (average 22%), due to additional computation required for encoding and decoding processes at every round. The reduction of the neurons from 32 to 8 (highlighted in bold) yields only a slight reduction of the F1-score at similar confidence, indicating that there is significant room for savings. Eventually, all of the aforementioned approaches reduced the size of the dataset over the round by more than 80% (from 90 KB down to 13.5 KB). Until this point, the presented results were from training when all samples in the training set were used in every \(vFL\) training round. Figure 16 illustrates the impact of reducing the batch size in the 8-neuron cut-layer case. Results for each scenario are obtained via at least 8 experiments. We observed the performance for various batch sizes also over different rounds on the test set. Using a randomly selected batch with a size of 32 (depicted via green line) samples and train for 3000 rounds yielded the highest savings in terms of both network footprint (from mean 13.5 KB to below 4 KB as annotated in Figure 16b) and training time (from 1313s to just above 300 s as depicted in Figure 16c) while sustaining the F1-score at around 0.86 as seen from Figure 16a. We also observed that random selection of batches as compared to selection of batches on an incremental index basis yielded a more robust training. We hypothesize that the reason for this is with random batch selection, we do not limit the model training always end up on the same batch at the last round of \(vFL\) training, and we avoid the model to customize on the exact same batch over multiple experiments. These examples show that a skilled fine-tuning of the \(vFL\) parameters has great potential for computing and transmission resource (and thus energy) savings without having to compromise on the F1-score.