Minimax Game for Training Generative Adversarial Networks
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OUTLINE
Game Theory
Game theory is a mathematical framework used to study strategic interactions between rational decision-makers.
Odd or Even
Players I and II simultaneously call out one of the numbers one or two. Player I’s name is Odd; he wins if the sum of the numbers is odd. Player II’s name is Even; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in dollars.
How we solve?
Minimax equation
The minimax strategy involves maximizing one's own payoff while simultaneously minimizing the opponent's potential payoff.
| B1 | B2 |
-----------------------------
A1 | (3,1) | (0,2) |
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A2 | (2,4) | (1,3) |
Generative Adversarial Networks (GANs)
GANs have trained two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G.
Minimax equation and GANs
It looks like this in the coding part
The discriminator's goal is to maximize
The 'errD_real' term corresponds to logD(x)
The 'errD_fake' term corresponds to log(1−D(G(z)))
The discriminator's loss 'errD' is the sum of these terms.
The generator's goal is to minimize
The 'errG' term corresponds to log(1−D(G(z)))
The generator's loss is 'errG'
References