Algorithm 2 Query Synthesis Active Learning

Input: A dataset $\mathcal{D}={\left\{(x_j,y_j)\right\}}_{j=1}^N$, a general active learning strategy S, a utility function u, number of iterations T, a discount factor $\gamma$ and a generation method for creating synthetic queries $GenerateQueryPoint()$. Output: A Learned model ${\theta }_T$ and a cumulative gained utility $u_T$. ${\mathcal{D}}_L\leftarrow$$N_{init}$ labeled data samples randomly chosen out of $\mathcal{D}$. Train the regression model using the initial training data to obtain initial model ${\theta }_0$. repeat  $x^{*}=GenerateQueryPoint(S,{\mathcal{D}}_U,{\theta }_i)$.  $y^{*}\leftarrow$ the true label for the query sample $x^{*}$.  Add the acquired data point $(x^{*},y^{*})$ to the training data: ${\mathcal{D}}_L\leftarrow {\mathcal{D}}_L\cup (x^{*},y^{*})$.  Evaluate the utility $u_i$ using the new acquired point: $u_i\leftarrow u(x^{*},y^{*})$.  Update the regression model ${\theta }_i$ using the new acquired point $(x^{*},y^{*})$. untilT iterations executed   return The learned model ${\theta }_T$ and the cumulative discounted utility $u_T={\sum }_{i=1}^T{\gamma }^{i-1}{u}_i$.