We introduce Implicit Policy, a general class of expressive policies that can flexibly represent complex action distributions in reinforcement learning, with efficient algorithms to compute entropy regularized policy gradients. We empirically show that, despite its simplicity in implementation, entropy regularization combined with a rich policy class can attain desirable properties displayed under maximum entropy reinforcement learning framework, such as robustness and multi-modality.
Implicit models have been extensively studied in probabilistic inference and generative modeling @cite_16 @cite_2 @cite_0 @cite_13 . Implicit models define distributions by transforming source noise via a forward pass of neural networks, which in general sacrifice tractable probability density for more expressive representation. Normalizing Flows are a special case of implicit models @cite_5 @cite_18 @cite_35 , where transformations from source noise to output are invertible and allow for maximum likelihood inference. Borrowing inspirations from prior works, we introduce implicit models into policy representation and empirically show that such rich policy class entails multi-modal behavior during training. In @cite_13 , GAN @cite_16 is used as an optimal density estimator for likelihood free inference. In our work, we apply similar idea to compute entropy regularization when policy density is not available.
@cite_35 @cite_18 @cite_0 @cite_2 @cite_5 @cite_16 @cite_13
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Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity. Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for models which encompass our understanding of the physical word. Despite this fundamental nature, the use of implicit models remains limited due to challenge in positing complex latent structure in them, and the ability to inference in such models with large data sets. In this paper, we first introduce the hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling thereby defining models via simulators of data with rich hidden structure. Next, we develop likelihood-free variational inference (LFVI), a scalable variational inference algorithm for HIMs. Key to LFVI is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. We demonstrate diverse applications: a large-scale physical simulator for predator-prey populations in ecology; a Bayesian generative adversarial network for discrete data; and a deep implicit model for symbol generation. We propose an adversarial training procedure for learning a causal implicit generative model for a given causal graph. We show that adversarial training can be used to learn a generative model with true observational and interventional distributions if the generator architecture is consistent with the given causal graph. We consider the application of generating faces based on given binary labels where the dependency structure between the labels is preserved with a causal graph. This problem can be seen as learning a causal implicit generative model for the image and labels. We devise a two-stage procedure for this problem. First we train a causal implicit generative model over binary labels using a neural network consistent with a causal graph as the generator. We empirically show that WassersteinGAN can be used to output discrete labels. Later, we propose two new conditional GAN architectures, which we call CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained causal implicit generative model for the labels is then a causal implicit generative model over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset. Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent structure in them, and in performing inferences in such models with large data sets. In this paper, we first introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data with rich hidden structure. Next, we develop likelihood-free variational inference (LFVI), a scalable variational inference algorithm for HIMs. Key to LFVI is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. We demonstrate diverse applications: a large-scale physical simulator for predator-prey populations in ecology; a Bayesian generative adversarial network for discrete data; and a deep implicit model for text generation. We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research. We introduce a generative model with multinomial likelihood and use Bayesian inference to learn this powerful generative model. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements. In this paper, we propose a novel generative model named Stacked Generative Adversarial Networks (SGAN), which is trained to invert the hierarchical representations of a bottom-up discriminative network. Our model consists of a top-down stack of GANs, each learned to generate lower-level representations conditioned on higher-level representations. A representation discriminator is introduced at each feature hierarchy to encourage the representation manifold of the generator to align with that of the bottom-up discriminative network, leveraging the powerful discriminative representations to guide the generative model. In addition, we introduce a conditional loss that encourages the use of conditional information from the layer above, and a novel entropy loss that maximizes a variational lower bound on the conditional entropy of generator outputs. We first train each stack independently, and then train the whole model end-to-end. Unlike the original GAN that uses a single noise vector to represent all the variations, our SGAN decomposes variations into multiple levels and gradually resolves uncertainties in the top-down generative process. Based on visual inspection, Inception scores and visual Turing test, we demonstrate that SGAN is able to generate images of much higher quality than GANs without stacking. In this paper, we propose a novel generative model named Stacked Generative Adversarial Networks (SGAN), which is trained to invert the hierarchical representations of a bottom-up discriminative network. Our model consists of a top-down stack of GANs, each learned to generate lower-level representations conditioned on higher-level representations. A representation discriminator is introduced at each feature hierarchy to encourage the representation manifold of the generator to align with that of the bottom-up discriminative network, leveraging the powerful discriminative representations to guide the generative model. In addition, we introduce a conditional loss that encourages the use of conditional information from the layer above, and a novel entropy loss that maximizes a variational lower bound on the conditional entropy of generator outputs. We first train each stack independently, and then train the whole model end-to-end. Unlike the original GAN that uses a single noise vector to represent all the variations, our SGAN decomposes variations into multiple levels and gradually resolves uncertainties in the top-down generative process. Based on visual inspection, Inception scores and visual Turing test, we demonstrate that SGAN is able to generate images of much higher quality than GANs without stacking. Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they provide samples that are sharp and compelling; and they allow us to harness our knowledge of building highly accurate neural network classifiers. Here, we develop our understanding of GANs with the aim of forming a rich view of this growing area of machine learning---to build connections to the diverse set of statistical thinking on this topic, of which much can be gained by a mutual exchange of ideas. We frame GANs within the wider landscape of algorithms for learning in implicit generative models---models that only specify a stochastic procedure with which to generate data---and relate these ideas to modelling problems in related fields, such as econometrics and approximate Bayesian computation. We develop likelihood-free inference methods and highlight hypothesis testing as a principle for learning in implicit generative models, using which we are able to derive the objective function used by GANs, and many other related objectives. The testing viewpoint directs our focus to the general problem of density ratio estimation. There are four approaches for density ratio estimation, one of which is a solution using classifiers to distinguish real from generated data. Other approaches such as divergence minimisation and moment matching have also been explored in the GAN literature, and we synthesise these views to form an understanding in terms of the relationships between them and the wider literature, highlighting avenues for future exploration and cross-pollination. We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements. The classic Generative Adversarial Net and its variants can be roughly categorized into two large families: the unregularized versus regularized GANs. By relaxing the non-parametric assumption on the discriminator in the classic GAN, the regularized GANs have better generalization ability to produce new samples drawn from the real distribution. It is well known that the real data like natural images are not uniformly distributed over the whole data space. Instead, they are often restricted to a low-dimensional manifold of the ambient space. Such a manifold assumption suggests the distance over the manifold should be a better measure to characterize the distinct between real and fake samples. Thus, we define a pullback operator to map samples back to their data manifold, and a manifold margin is defined as the distance between the pullback representations to distinguish between real and fake samples and learn the optimal generators. We justify the effectiveness of the proposed model both theoretically and empirically. Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at this https URL We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. Auto-encoding generative adversarial networks (GANs) combine the standard GAN algorithm, which discriminates between real and model-generated data, with a reconstruction loss given by an auto-encoder. Such models aim to prevent mode collapse in the learned generative model by ensuring that it is grounded in all the available training data. In this paper, we develop a principle upon which auto-encoders can be combined with generative adversarial networks by exploiting the hierarchical structure of the generative model. The underlying principle shows that variational inference can be used a basic tool for learning, but with the in- tractable likelihood replaced by a synthetic likelihood, and the unknown posterior distribution replaced by an implicit distribution; both synthetic likelihoods and implicit posterior distributions can be learned using discriminators. This allows us to develop a natural fusion of variational auto-encoders and generative adversarial networks, combining the best of both these methods. We describe a unified objective for optimization, discuss the constraints needed to guide learning, connect to the wide range of existing work, and use a battery of tests to systematically and quantitatively assess the performance of our method. In this paper, we propose a model using generative adversarial net (GAN) to generate realistic text. Instead of using standard GAN, we combine variational autoencoder (VAE) with generative adversarial net. The use of high-level latent random variables is helpful to learn the data distribution and solve the problem that generative adversarial net always emits the similar data. We propose the VGAN model where the generative model is composed of recurrent neural network and VAE. The discriminative model is a convolutional neural network. We train the model via policy gradient. We apply the proposed model to the task of text generation and compare it to other recent neural network based models, such as recurrent neural network language model and SeqGAN. We evaluate the performance of the model by calculating negative log-likelihood and the BLEU score. We conduct experiments on three benchmark datasets, and results show that our model outperforms other previous models. Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to transfer techniques across research lines in a principled way. For example, we apply the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism that leverages generated samples. Experiments show generality and effectiveness of the transferred techniques. Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5]. Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images. But many of these methods, including generative adversarial networks (GANs), can be difficult to train, in part because they are prone to mode collapse, which means that they characterize only a few modes of the true distribution. To address this, we introduce VEEGAN, which features a reconstructor network, reversing the action of the generator by mapping from data to noise. Our training objective retains the original asymptotic consistency guarantee of GANs, and can be interpreted as a novel autoencoder loss over the noise. In sharp contrast to a traditional autoencoder over data points, VEEGAN does not require specifying a loss function over the data, but rather only over the representations, which are standard normal by assumption. On an extensive set of synthetic and real world image datasets, VEEGAN indeed resists mode collapsing to a far greater extent than other recent GAN variants, and produces more realistic samples. Two recently introduced criteria for estimation of generative models are both based on a reduction to binary classification. Noise-contrastive estimation (NCE) is an estimation procedure in which a generative model is trained to be able to distinguish data samples from noise samples. Generative adversarial networks (GANs) are pairs of generator and discriminator networks, with the generator network learning to generate samples by attempting to fool the discriminator network into believing its samples are real data. Both estimation procedures use the same function to drive learning, which naturally raises questions about how they are related to each other, as well as whether this function is related to maximum likelihood estimation (MLE). NCE corresponds to training an internal data model belonging to the discriminator network but using a fixed generator network. We show that a variant of NCE, with a dynamic generator network, is equivalent to maximum likelihood estimation. Since pairing a learned discriminator with an appropriate dynamically selected generator recovers MLE, one might expect the reverse to hold for pairing a learned generator with a certain discriminator. However, we show that recovering MLE for a learned generator requires departing from the distinguishability game. Specifically: (i) The expected gradient of the NCE discriminator can be made to match the expected gradient of MLE, if one is allowed to use a non-stationary noise distribution for NCE, (ii) No choice of discriminator network can make the expected gradient for the GAN generator match that of MLE, and (iii) The existing theory does not guarantee that GANs will converge in the non-convex case. This suggests that the key next step in GAN research is to determine whether GANs converge, and if not, to modify their training algorithm to force convergence. As a new way of training generative models, Generative Adversarial Nets (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is non-trivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines. As a new way of training generative models, Generative Adversarial Net (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is nontrivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines.