text: In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although many research studies have been devoted to making predictions on a single entity, it remains an open challenge to forecast future behaviors for multiple interactive agents simultaneously. In this work, we take advantage of the Generative Adversarial Network (GAN) due to its capability of distribution learning and propose a generic multi-agent probabilistic prediction and tracking framework which takes the interactions among multiple entities into account, in which all the entities are treated as a whole. However, since GAN is very hard to train, we make an empirical research and present the relationship between training performance and hyperparameter values with a numerical case study. The results imply that the proposed model can capture both the mean, variance and multi-modalities of the groundtruth distribution. Moreover, we apply the proposed approach to a real-world task of vehicle behavior prediction to demonstrate its effectiveness and accuracy. The results illustrate that the proposed model trained by adversarial learning can achieve a better prediction performance than other state-of-the-art models trained by traditional supervised learning which maximizes the data likelihood. The well-trained model can also be utilized as an implicit proposal distribution for particle filtered based Bayesian state estimation.
  @cite_13: We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.
  @cite_18: In recent years, supervised learning with convolutional networks (CNNs) has seen huge adoption in computer vision applications. Comparatively, unsupervised learning with CNNs has received less attention. In this work we hope to help bridge the gap between the success of CNNs for supervised learning and unsupervised learning. We introduce a class of CNNs called deep convolutional generative adversarial networks (DCGANs), that have certain architectural constraints, and demonstrate that they are a strong candidate for unsupervised learning. Training on various image datasets, we show convincing evidence that our deep convolutional adversarial pair learns a hierarchy of representations from object parts to scenes in both the generator and discriminator. Additionally, we use the learned features for novel tasks - demonstrating their applicability as general image representations.
  @cite_26: Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the gradient descent'' form of GAN optimization, i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator parameters. We show that even though GAN optimization does correspond to a convex-concave game (even for simple parameterizations), under proper conditions, equilibrium points of this optimization procedure are still for the traditional GAN formulation. On the other hand, we show that the recently proposed Wasserstein GAN can have non-convergent limit cycles near equilibrium. Motivated by this stability analysis, we propose an additional regularization term for gradient descent GAN updates, which able to guarantee local stability for both the WGAN and the traditional GAN, and also shows practical promise in speeding up convergence and addressing mode collapse.
  @cite_22: Generative Adversarial Nets [8] were recently introduced as a novel way to train generative models. In this work we introduce the conditional version of generative adversarial nets, which can be constructed by simply feeding the data, y, we wish to condition on to both the generator and discriminator. We show that this model can generate MNIST digits conditioned on class labels. We also illustrate how this model could be used to learn a multi-modal model, and provide preliminary examples of an application to image tagging in which we demonstrate how this approach can generate descriptive tags which are not part of training labels.
  @cite_7: Generative adversarial networks have been proposed as a way of efficiently training deep generative neural networks. We propose a generative adversarial model that works on continuous sequential data, and apply it by training it on a collection of classical music. We conclude that it generates music that sounds better and better as the model is trained, report statistics on generated music, and let the reader judge the quality by downloading the generated songs.
  @cite_8: 
  @cite_9: Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their application to medical data. RGANs make use of recurrent neural networks (RNNs) in the generator and the discriminator. In the case of RCGANs, both of these RNNs are conditioned on auxiliary information. We demonstrate our models in a set of toy datasets, where we show visually and quantitatively (using sample likelihood and maximum mean discrepancy) that they can successfully generate realistic time-series. We also describe novel evaluation methods for GANs, where we generate a synthetic labelled training dataset, and evaluate on a real test set the performance of a model trained on the synthetic data, and vice-versa. We illustrate with these metrics that RCGANs can generate time-series data useful for supervised training, with only minor degradation in performance on real test data. This is demonstrated on digit classification from ‘serialised’ MNIST and by training an early warning system on a medical dataset of 17,000 patients from an intensive care unit. We further discuss and analyse the privacy concerns that may arise when using RCGANs to generate realistic synthetic medical time series data, and demonstrate results from differentially private training of the RCGAN.
  @cite_19: This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that also maximizes the mutual information between a small subset of the latent variables and the observation. We derive a lower bound of the mutual information objective that can be optimized efficiently. Specifically, InfoGAN successfully disentangles writing styles from digit shapes on the MNIST dataset, pose from lighting of 3D rendered images, and background digits from the central digit on the SVHN dataset. It also discovers visual concepts that include hair styles, presence absence of eyeglasses, and emotions on the CelebA face dataset. Experiments show that InfoGAN learns interpretable representations that are competitive with representations learned by existing supervised methods. For an up-to-date version of this paper, please see https: arxiv.org abs 1606.03657.
  @cite_5: In this paper, we analyze the numerics of common algorithms for training Generative Adversarial Networks (GANs). Using the formalism of smooth two-player games we analyze the associated gradient vector field of GAN training objectives. Our findings suggest that the convergence of current algorithms suffers due to two factors: i) presence of eigenvalues of the Jacobian of the gradient vector field with zero real-part, and ii) eigenvalues with big imaginary part. Using these findings, we design a new algorithm that overcomes some of these limitations and has better convergence properties. Experimentally, we demonstrate its superiority on training common GAN architectures and show convergence on GAN architectures that are known to be notoriously hard to train.
  @cite_10: 
summary: The core idea of training a deep generative model by making it compete with an opponent discriminator model was proposed in @cite_8 where a two-player minimax game is formulated. A straightforward extension of incorporating condition information into both generator and discriminator was put forward in @cite_22 in which the generator can produce realistic images of particular categories. There are mainly two aspects that can be modified to enhance the stability of GAN training: model setup @cite_18 @cite_10 @cite_19 and optimization method @cite_13 @cite_26 @cite_5 . Although there have been a large number of studies on realistic image generation tasks which provided promising results, much fewer research efforts, to our knowledge, have been devoted to continuous time-series data generation with adversarial training @cite_7 @cite_9 . Our task is different from existing works where the generators are trained in unsupervised learning settings without any visualizable groundtruth distribution. This makes it hard to evaluate the learning performance. On the contrary, in this work the groundtruth actions can be utilized to monitor the training quality by calculating a proper error metric as well as provide a heuristic during the training process.