# Deep Active Learning for Computer Vision Tasks: Methodologies, Applications, and Challenges
## 4 Deep Active Learning Methods
### Generative Adversarial Active Learning  
According to the analysis of [55], the _Core-Set_ strategy [48] is very inefficient in high-dimensional representation learning due to its inherent distance-based computation. This obstacle is well addressed by leveraging GAN or VAE for representation learning from high-dimensional data. Generative Adversarial Networks (GAN) is a novel representation learning method proposed by [PERSON] [56]. Its core idea is \"Generative\" and \"Adversarial\". The GAN network structure contains two models. One is the generator \(\mathbb{G}\) and the other is the discriminator \(\mathbb{D}\). The generator generally uses a deconvolutional neural network or a fully connected neural network to synthesize new data (e.g., images). At the same time, the discriminator is a CNN-based binary classifier to distinguish whether the input is from the natural distribution or synthesized one from the generator. The discriminator is trained first to make a good judgment so that the real and generated samples can be better distinguished. Then the parameters of the generator can be updated more accurately. The goal of discriminator is that \(P(\mathbb{D}(x)|x\in\textit{real})=1\) while \(P(\mathbb{D}(x)|x\in\textit{fake})=0\). Then the generator and discriminator in GANs are trained against each other in a two-player game. The weights and biases of the discriminator and generator are trained through back-propagation until they reach a dynamic equilibrium state with unlabeled samples. In order to discriminate samples and classify them, the discriminator usually utilizes the cross-entropy loss to measure similarity, which is formulated as follows [56]:  
\[\mathcal{L}_{\mathbb{D}}=\frac{1}{N}\sum_{i=1}^{N}\Bigl{[}\log\mathbb{D}\Big{(} \boldsymbol{x}^{(i)}\Big{)}+\log\Bigl{(}1-\mathbb{D}\Big{(}\mathbb{G}\Big{(} \boldsymbol{z}^{(i)}\Big{)}\Big{)}\Bigr{)}\Bigr{]} \tag{4}\]  
\[\mathcal{L}_{\mathbb{G}}=\frac{1}{N}\sum_{i=1}^{N}\log\Bigl{(}1-\mathbb{D} \Big{(}\mathbb{G}\Big{(}\boldsymbol{z}^{(i)}\Big{)}\Big{)}\Bigr{)} \tag{5}\]  
\(\boldsymbol{z}\sim p_{\boldsymbol{z}}(\boldsymbol{z})\) is the generated distribution and \(\boldsymbol{x}\sim p_{\text{data}}(\boldsymbol{x})\) is the real distribution. \(N\) denotes the batch size. As a consequence, the objective function of GAN is shown as follows [56]:  
\[\mathcal{L}=\arg\min_{\mathbb{G}}\max_{\mathbb{D}}V(\mathbb{G},\mathbb{D})= \mathbb{E}_{\boldsymbol{x}\sim p_{\text{data}}(\boldsymbol{x})}[\log\mathbb{ D}(\boldsymbol{x})]+\mathbb{E}_{\boldsymbol{z}\sim p_{\boldsymbol{z}}( \boldsymbol{z})}[\log(1-\mathbb{D}(\mathbb{G}(\boldsymbol{z})))], \tag{6}\]  
where \(V(\mathbb{G},\mathbb{D})\) is the difference between the generated distribution \(p_{\boldsymbol{z}}\) and the actual distribution \(p_{\text{data}}\). \(\max\) is to train the discriminator to discriminate the sample to the greatest extent. \(\min\) is to train the generator to minimize the difference between the generated sample and the actual sample. When the algorithm converges, the samples generated by the generator can confuse the discriminator and cannot distinguish right from wrong. In other words, the generator should try its best to generate more realistic results to deceive the discriminator. The discriminator should try its best to distinguish the truth from the false and not be deceived by the generator. The network reaches the ideal state when the generated result is actual (discrimination probability is 0.5). [PERSON] et al. [57] firstly proposed a novel query synthesis-based active learning method GAAL fused with GAN. GAAL was trained on datasets MNIST [41] (achieving accuracy 70.44%) and CIFAR-10 [47] while tested on the dataset USPS [58]. The workflow of GAAL can be concluded as Algorithm 2. ```
Input : A labeled data pool \(L\), an unlabeled data pool \(\mathcal{U}\), annotators \(A\), a generator \(\mathbb{G}\) and a discriminator \(\mathbb{D}\). Output : A well-trained model \(\mathcal{M}\) with the least labeling cost.