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Register a new userVariational Inference for Data-Efficient Model Learning in POMDPs
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Partially observable Markov decision processes (POMDPs) are a powerful abstraction for tasks that require decision making under uncertainty, and capture a wide range of real world tasks. Today, effective planning approaches exist that generate effective strategies given black-box models of a POMDP task. Yet, an open question is how to acquire accurate models for complex domains. In this paper we propose DELIP, an approach to model learning for POMDPs that utilizes amortized structured variational inference. We empirically show that our model leads to effective control strategies when coupled with state-of-the-art planners. Intuitively, model-based approaches should be particularly beneficial in environments with changing reward structures, or where rewards are initially unknown. Our experiments confirm that DELIP is particularly effective in this setting.
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Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep learning algorithms are lacking of theoretical support. On the other hand, another line of works have proposed theoretical frameworks that are computationally infeasible. In this paper, we train sparse deep neural networks with a fully Bayesian treatment under spike-and-slab priors, and develop a set of computationally efficient variational inferences via continuous relaxation of Bernoulli distribution. The variational posterior contraction rate is provided, which justifies the consistency of the proposed variational Bayes method. Notably, our empirical results demonstrate that this variational procedure provides uncertainty quantification in terms of Bayesian predictive distribution and is also capable to accomplish consistent variable selection by training a sparse multi-layer neural network.
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing inputs and their locations across layers. In this paper, we simplify the training by setting the locations to a fixed subset of data and sampling the inducing inputs from a variational distribution. This reduces the trainable parameters and computation cost without significant performance degradations, as demonstrated by our empirical results on regression problems. Our modifications simplify and stabilize DGP training while making it amenable to sampling schemes for setting the inducing inputs.
This paper studies the fundamental problem of learning deep generative models that consist of multiple layers of latent variables organized in top-down architectures. Such models have high expressivity and allow for learning hierarchical representations. Learning such a generative model requires inferring the latent variables for each training example based on the posterior distribution of these latent variables. The inference typically requires Markov chain Monte Caro (MCMC) that can be time consuming. In this paper, we propose to use noise initialized non-persistent short run MCMC, such as finite step Langevin dynamics initialized from the prior distribution of the latent variables, as an approximate inference engine, where the step size of the Langevin dynamics is variationally optimized by minimizing the Kullback-Leibler divergence between the distribution produced by the short run MCMC and the posterior distribution. Our experiments show that the proposed method outperforms variational auto-encoder (VAE) in terms of reconstruction error and synthesis quality. The advantage of the proposed method is that it is simple and automatic without the need to design an inference model.
Neural Network based controllers hold enormous potential to learn complex, high-dimensional functions. However, they are prone to overfitting and unwarranted extrapolations. PAC Bayes is a generalized framework which is more resistant to overfitting and that yields performance bounds that hold with arbitrarily high probability even on the unjustified extrapolations. However, optimizing to learn such a function and a bound is intractable for complex tasks. In this work, we propose a method to simultaneously learn such a function and estimate performance bounds that scale organically to high-dimensions, non-linear environments without making any explicit assumptions about the environment. We build our approach on a parallel that we draw between the formulations called ELBO and PAC Bayes when the risk metric is negative log likelihood. Through our experiments on multiple high dimensional MuJoCo locomotion tasks, we validate the correctness of our theory, show its ability to generalize better, and investigate the factors that are important for its learning. The code for all the experiments is available at https://bit.ly/2qv0JjA.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical Dirichlet process hidden Markov models, and to any datasets generated by emission distributions in the exponential family. Our experiment results on two discrete datasets show that our inference is both more efficient and more accurate than its uncollapsed version, stochastic variational inference.
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