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What is the confusion loss used in domain adaptation (DA) for adversarial learning/GANs? See this paper.

Two domains:

  • $s$: source domain
  • $t$: target domain

Generator/Discriminator setting:

  • $M_s:x_s\rightarrow f_t$ generator of feature for the source domain; and $M_t: x_t\rightarrow f_t$ generator of feature for the target domain
  • $D:f\rightarrow [0,1]$: discriminator, 1 if the features came from the source domain, 0 if from the target domain

The generator tries to minimize (equation (8) in the paper):

$\mathcal{L}_{\mathrm{adv}_{M}}\left(\mathbf{X}_{s}, \mathbf{X}_{t}, D\right)=$ $-\sum_{d \in\{s, t\}} \mathbb{E}_{\mathbf{x}_{d} \sim \mathbf{X}_{d}}\left[\frac{1}{2} \log D\left(M_{d}\left(\mathbf{x}_{d}\right)\right)\right.$ $\left.+\frac{1}{2} \log \left(1-D\left(M_{d}\left(\mathbf{x}_{d}\right)\right)\right)\right]$

If the samples come from $s$, then $d=s$; the generator tries to maximize the first part $\log D(M_s(x_s))$, which is doing the same thing as the discriminator? And tries to maximize $\log(1-D(M_s(x_s))$, which is the classical generator loss function (so the opposite of the first part, and I do not understand that). And the inverse for when $d=t$.

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