text: Generative Adversarial Networks (GANs) are a machine learning approach capable of generating novel example outputs across a space of provided training examples. Procedural Content Generation (PCG) of levels for video games could benefit from such models, especially for games where there is a pre-existing corpus of levels to emulate. This paper trains a GAN to generate levels for Super Mario Bros using a level from the Video Game Level Corpus. The approach successfully generates a variety of levels similar to one in the original corpus, but is further improved by application of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Specifically, various fitness functions are used to discover levels within the latent space of the GAN that maximize desired properties. Simple static properties are optimized, such as a given distribution of tile types. Additionally, the champion A* agent from the 2009 Mario AI competition is used to assess whether a level is playable, and how many jumping actions are required to beat it. These fitness functions allow for the discovery of levels that exist within the space of examples designed by experts, and also guide the search towards levels that fulfill one or more specified objectives.
  @cite_6: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train 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. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
summary: Generative Adversarial Networks (GANs) were first introduced by Goodfellow @cite_6 in 2014. Their training process can be seen as a two-player adversarial game in which a generator @math (faking samples decoded from a random noise vector) and a discriminator @math (distinguishing real fake samples and outputting 0 or 1) are trained at the same time by playing against each other. The discriminator @math aims at minimizing the probability of mis-judgment, while the generator @math aims at maximizing that probability. Thus, the generator is trained to deceive the discriminator by generating samples that are good enough to be classified as genuine. Training ideally reaches a steady state where @math reliably generates realistic examples and @math is no more accurate than a coin flip.