# A Generative Adversarial Network for Financial Advisor Recruitment in Smart Crowdsourcing Platforms
## 4 Results and Discussions
### Generative Adversarial Networks' Training Process  
We construct a database containing pairs of financial advisors and investors. The training data set contains \(N=412\),\(448\) rows, each row of this data set contains the investor profile and the associated 'ideal' financial advisors' signature that corresponds to that investor identified from the financial advisor and investor data sets presented in Section 4. Hence, the training data set of the GAN is composed of \(N\) pairs of \((i,f_{i}^{*})\in\mathcal{I}\times\mathcal{F}\), where \(i\) the investor profile and \(f_{i}^{*}\) is the ideal financial advisors' profile associated to investor \(i\). In practice, for generating the training data set, the ideal advisor for each investor is determined based on the activities and experiences within the smart crowdsourcing platforms. In our case, we determined them based on a machine learning algorithm proposed in [44]. The training of the GANs is performed as follows: first, the investor profile is fed as a noise to the generator \(\mathcal{G}\). Then, from this noise, \(\mathcal{G}\) generates a two-dimensional gray-scale image that represents the financial advisors signature. Afterwards, the generated image is fed to the discriminator \(\mathcal{D}\). The latter classifies the image as real if the image is close to the targeted financial advisor's signature or False if not. Then, the classification result will be forwarded as a feedback to \(\mathcal{G}\), which will use the provided feedback to update his weights, and hence after a certain number of training iterations, \(\mathcal{G}\) learns how to automatically output the ideal financial advisors' profile. The GAN training process was performed over \(e=70\) epochs and the data set was divided on \(b=3200\) batches and hence, for each epoch, \(i_{e}=\frac{N}{b}=128\) iterations are performed for a total \(l_{it}=e\times i_{e}=8960\) iterations during the training process. The evolution of the loss functions of the two models of the GAN is represented in Figure 7. In this figure, the adversarial relationship of the two models is shown. For instance, when the \(\mathcal{D}\) is fooled by the fake images generated by \(\mathcal{G}\), i.e., the loss function of \(\mathcal{D}\) is high, we can see that the loss function of \(\mathcal{G}\) is low and vice versa. This behavior proves that the trained GAN has avoided one of the most challenging problems of the training: mode collapse. Mode collapse happens when the generator learns a specific distribution that always fools the discriminator and keeps generating the same sample each time; however, since our loss functions behave in the way described earlier, we can confirm that the GAN training was successful. The discriminator and the generator were in a continuous game and both of them have efficiently converged. After 8000 iterations, the two models reach stability and both loss functions converge to a stable value. In fact, the behavior of GANs in training is very different from the one of regular Artificial Neural Networks (ANNs). The adversarial training with GANs does not necessarily mean that both the generator and discriminator will achieve clear improvement of their respective loss functions, which can be observed in Figure 7 where the convergence values at the end of the training are close to the initial settings. Similar observations are noticed in many previous work that employed GAN models [61, 62]. To better prove the convergence of the GAN, we perform, at the end of each training iteration, tests on a sample of 500 combinations of investors and financial advisors to measure the resulting pixel-wise Mean Absolute Error (MAE) at that stage of training. In other words, after the end of each iteration, we use the partially trained \(\mathcal{G}\) to  
Figure 6: Histogram representation showing the distribution of the investor data set features: salary, age, and investment budget. generate optimal advisors' signatures for the test samples.