The GAN Hinge Loss is a hinge loss based loss function for generative adversarial networks:
L_D=−E_(x,y)∼p_data[min(0,−1+D(x,y))]−E_z∼p_z,y∼p_data[min(0,−1−D(G(z),y))]L\_{D} = -\mathbb{E}\_{\left(x, y\right)\sim{p}\_{data}}\left[\min\left(0, -1 + D\left(x, y\right)\right)\right] -\mathbb{E}\_{z\sim{p\_{z}}, y\sim{p\_{data}}}\left[\min\left(0, -1 - D\left(G\left(z\right), y\right)\right)\right]L_D=−E_(x,y)∼p_data[min(0,−1+D(x,y))]−E_z∼p_z,y∼p_data[min(0,−1−D(G(z),y))]
L_G=−E_z∼p_z,y∼p_dataD(G(z),y)L\_{G} = -\mathbb{E}\_{z\sim{p\_{z}}, y\sim{p\_{data}}}D\left(G\left(z\right), y\right)L_G=−E_z∼p_z,y∼p_dataD(G(z),y)