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The objective function (here for [LSGAN](https://paperswithcode.com/method/lsgan)) can be defined as:\r\n\r\n$$ \\min\\_{D}V\\_{LS}\\left(D\\right) = \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{x} \\sim p\\_{data}\\left(\\mathbf{x}\\right)}\\left[\\left(D\\left(\\mathbf{x}\\right) - b\\right)^{2}\\right] + \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{z}\\sim p\\_{data}\\left(\\mathbf{z}\\right)}\\left[\\left(D\\left(G\\left(\\mathbf{z}\\right)\\right) - a\\right)^{2}\\right] $$\r\n\r\n$$ \\min\\_{G}V\\_{LS}\\left(G\\right) = \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{z} \\sim p\\_{\\mathbf{z}}\\left(\\mathbf{z}\\right)}\\left[\\left(D\\left(G\\left(\\mathbf{z}\\right)\\right) - c\\right)^{2}\\right] $$\r\n\r\nwhere $a$ and $b$ are the labels for fake data and real data and $c$ denotes the value that $G$ wants $D$ to believe for fake data.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Least Squares Generative Adversarial 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