The full objective function is a weighted sum of both the adversarial loss and the cycle consistency loss, which is represented as follows:

Here, is the first adversarial loss and is the second adversarial loss. The first adversarial loss is calculated on the generator A, and the discriminator B. The second adversarial loss is calculated on the generator B, and the discriminator A. 

To train a CycleGAN, we need to optimize the following function:

The previous equation shows that, to train a CycleGAN, you need to minimize the losses of the generator networks and maximize the losses of the discriminator networks. After the optimization, we will get a set of trained networks that are capable of generating photos from paintings.