IEEE Circuits and Systems Magazine - Q4 2020 - 72

V. From Game Theory to GANs
This section mainly focuses on generative adversarial
network (GAN) and how it is motivated from the perspective of learning strategy.
A. Motivation on Learning Strategy of GAN
Although classic generative models, such as hidden
Markov models [51] and deep belief networks [12], have
been successfully applied in various fields, they still have
some inevitable limitations. Generally, generative models
are based on the principle of maximum likelihood, that is
to find a model that estimates a probability distribution
which approximates the distribution of the real data [52].
From this point of view, defining a probability density explicitly to describe the data distribution is convenient due
to the tractability of given density function in the computation of maximum likelihood estimation. However, it is
hard for the defined probability density to capture the
characteristics of real data perfectly and represent the
complexity of high-dimensional data distribution [53].
To avoid the drawbacks mentioned above, another
approach is to represent the probability density implicitly in a data-driven way. Inspired by the theory of zerosum game, a novel learning strategy, termed adversarial
learning, is developed to help neural network learn a
probability distribution which approximates the real data
distribution [13]. The network framework corresponding
to adversarial learning is generative adversarial networks
(GAN). Through adversarial learning, two neural networks
(generator and discriminator) in GAN are optimized with
two opposite objectives: one is responsible for learning to
generate samples to deceive the other while the other is
trained not to be deceived. According to game theory, the
competition between the two networks can reach Nash
equilibrium at last, means the data distribution is learned
by generator network successfully [52].

B. Details of Architecture
As mentioned above, GAN consists of two competing
sub-models: the generative model G (i.e. generator) and
the discriminative model D (i.e. discriminator). Technically, GAN is rather a framework than a neural network.
Like the encoder-decoder framework, the two sub-models of GAN can be constructed flexibly with various neural network models. In vanilla GAN [13], the generator
and discriminator are both multi-layer perceptrons.
The learning process of GAN is modeled as a game (see
Fig. 5). In this game, G is in charge of yielding a sample
G ^z h according to a stochastic noise z ~ p noise to deceive
the discriminator, where pnoise is the distribution of the
stochastic noise. Then, D differentiates the sample G ^z h
from a real sample x ~ p data, where pdata is the distribution of the real dataset. Specifically, the discriminator D
takes as input both the fake sample G ^z h and a real sample x ~ p data . For G ^z h , D gives 0 as a negative response.
While for x ~ p data, D outputs 1 as a positive response. It
can be proved that when the generator and discriminator
are trained sufficiently, the model G can learn a distribution that approaches the real data distribution pdata [13].
In this case, both D ^x h and D (G ((z))) are close to 0.5,
which means D can no longer recognize which sample is
real. This process can be summarized as a minimax game
between D and G and the objective function O(D, G) is:
	

min maxO ^ D, G h = E x~p data 6logD ^x h@ +
G

E z~p noise 6log ^1 - D ^G ^z hhh@, (15)

D

or
	

min maxO ^ D, G h = E x~p data 6logD ^xh@ +
G

D

E z~p noise 6- log ^ D ^G ^z hhh@ . (16)

The GAN framework is innovative as it replaces the
variational lower bounds or Markov chains with supervised learning to approximate the distribution of real data

Step 1
Z

G (Z )

Generator

Discriminator

Loss G

Step 2
X

X

G (Z )

Discriminator

Loss D

Figure 5. The training process of GAN can be divided into two iterative steps: 1) fixing the parameters of the discriminator and
training the generator; 2) training the discriminator using a real sample x and a generated sample G(Z).
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IEEE Circuits and Systems Magazine - Q4 2020

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