Abstraction is crucial for effective sequential decision making in domains with large state spaces. In this work, we propose an information bottleneck method for learning approximate bisimulations, a type of state abstraction. We use a deep neural encoder to map states onto continuous embeddings. We map these embeddings onto a discrete representation using an action-conditioned hidden Markov model, which is trained end-to-end with the neural network. Our method is suited for environments with high-dimensional states and learns from a stream of experience collected by an agent acting in a Markov decision process. Through this learned discrete abstract model, we can efficiently plan for unseen goals in a multi-goal Reinforcement Learning setting. We test our method in simplified robotic manipulation domains with image states. We also compare it against previous model-based approaches to finding bisimulations in discrete grid-world-like environments. Source code is available at https://github.com/ondrejba/discrete_abstractions.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
While the difficulty of reinforcement learning problems is typically related to the complexity of their state spaces, Abstraction proposes that solutions often lie in simpler underlying latent spaces. Prior works have focused on learning either a continuous or dense abstraction, or require a human to provide one. Information-dense representations capture features irrelevant for solving tasks, and continuous spaces can struggle to represent discrete objects. In this work we automatically learn a sparse discrete abstraction of the underlying environment. We do so using a simple end-to-end traina…
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the posterior and the variational approximation, we minimize a semi-discrete optimal transport divergence. The solution of the resulting optimal transport problem provides both a particle approximation and a set of optimal transportation densities that map each particle to a segment of…
Vrije Universiteit Brussel（布鲁塞尔自由大学）；University of Antwerp – Flanders Make（安特卫普大学–法兰德斯制造）
We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in the limit. While these guarantees are valuable, they are insufficient for safety-critical applications. Furthermore, they are lost when applying advanced techniques such as deep-RL. To recover guarantees when applying advanced RL algorithms to more complex environments with (i) reachability, (ii) safety-constrained reachability, or (iii) discounted-reward obje…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；University of Helsinki（赫尔辛基大学）
Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Handling discrete latent variables is then challenging because the sampling process is not differentiable. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one, causing problems especially with models havi…
University of British Columbia（不列颠哥伦比亚大学）；MIT（麻省理工学院）
We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in var…
Department of Computer Science, Brown University（布朗大学计算机科学系）
Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good representations" to be a learned state abstraction, and "challenging problems" to be continuous control tasks. Our main contribution is a learning algorithm that abstracts a continuous state-space into a discrete one. We transfer this learned representation to unseen problems to enable effective learning. We provide theory showing that learned abstractions maint…
Microsoft Research（微软研究院）；Imperial College London（伦敦帝国理工学院）
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 w…
University of Cambridge（剑桥大学）；HHMI Janelia Research Campus（HHMI珍妮亚研究园区）
Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully exploits GPU parallelism. However, such simple approximate posteriors are often insufficient, as they eliminate statistical dependencies in the posterior. While it is possible to use normalizing flow approximate posteriors for continuous latents, some problems have discrete latents and strong statistical dependencies. The most natural approach to model these depe…
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions, on which the gradient-free SVGD is applied to perform efficient approximate inference. The empirical results show that our method outperforms traditional a…
McGill University（麦吉尔大学）；Mila, Quebec AI Institute（魁北克人工智能研究所Mila）；University of Montreal（蒙特利尔大学）；Beijing Institute of Technology（北京理工大学）；Harvard University（哈佛大学）；DeepMind；Microsoft Research（微软研究院）
Goal-conditioned reinforcement learning (RL) is a promising direction for training agents that are capable of solving multiple tasks and reach a diverse set of objectives. How to \textit{specify} and \textit{ground} these goals in such a way that we can both reliably reach goals during training as well as generalize to new goals during evaluation remains an open area of research. Defining goals in the space of noisy and high-dimensional sensory inputs poses a challenge for training goal-conditioned agents, or even for generalization to novel goals. We propose to address this by learning factor…
Calorimeter simulation is the most computationally expensive part of Monte Carlo generation of samples necessary for analysis of experimental data at the Large Hadron Collider (LHC). The High-Luminosity upgrade of the LHC would require an even larger amount of such samples. We present a technique based on Discrete Variational Autoencoders (DVAEs) to simulate particle showers in Electromagnetic Calorimeters. We discuss how this work paves the way towards exploration of quantum annealing processors as sampling devices for generation of simulated High Energy Physics datasets.
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact inference is often intractable. Markov chain Monte Carlo techniques make approximate inference possible, but the computational cost is prohibitive on the large data sets now becoming routinely available. Variational methods provide a deterministic alternative for approximation of the posterior distribution. We derive variational procedures for empirical Bayes a…
Goal-Oriented Skill Abstraction for Offline Multi-Task Reinforcement Learning
C2DL, Institute of Automation, Chinese Academy of Sciences（C2DL，自动化研究所，中国科学院）；School of Artificial Intelligence, University of Chinese Academy of Sciences（人工智能学院，中国科学院大学）；Tencent AI Lab（腾讯AI实验室）；Tsinghua University（清华大学）
Mila, Université de Montréal（米拉，蒙特利尔大学）；Kakao Brain；Rutgers University（罗格斯大学）
We introduce a variational approach to learning and inference of temporally hierarchical structure and representation for sequential data. We propose the Variational Temporal Abstraction (VTA), a hierarchical recurrent state space model that can infer the latent temporal structure and thus perform the stochastic state transition hierarchically. We also propose to apply this model to implement the jumpy-imagination ability in imagination-augmented agent-learning in order to improve the efficiency of the imagination. In experiments, we demonstrate that our proposed method can model 2D and 3D vis…
University of Oxford（牛津大学）；J. P. Morgan AI Research（摩根大通AI研究院）
We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by $N$ identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution and service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem as a discrete time Markov Decision Process (MDP) with a hybrid…
Discrete choice models describe the choices made by decision makers among alternatives and play an important role in transportation planning, marketing research and other applications. The mixed multinomial logit (MMNL) model is a popular discrete choice model that captures heterogeneity in the preferences of decision makers through random coefficients. While Markov chain Monte Carlo methods provide the Bayesian analogue to classical procedures for estimating MMNL models, computations can be prohibitively expensive for large datasets. Approximate inference can be obtained using variational met…
Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variational bound to efficiently train with Boltzmann machine priors. Using this bound, we develop DVAE++, a generative model with a global discrete prior and a hierarchy of convolutional continuous variables. …
Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an $\arg \max$ operation and is non-differentiable. In contrast to previous works which resort to softmax-based relaxations, we propose to optimize it directly by applying the direct loss minimization approach. Our proposal extends naturally to structured discrete latent variable models when evaluating the $\arg \max$…
Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete latent variables using the variational autoencoder framework, including backpropagation through the discrete latent variables. The associated class of probabilistic models comprises an undirected discrete component and a directed hierarchical continuous component. The discrete compon…
Boltzmann machines are powerful distributions that have been shown to be an effective prior over binary latent variables in variational autoencoders (VAEs). However, previous methods for training discrete VAEs have used the evidence lower bound and not the tighter importance-weighted bound. We propose two approaches for relaxing Boltzmann machines to continuous distributions that permit training with importance-weighted bounds. These relaxations are based on generalized overlapping transformations and the Gaussian integral trick. Experiments on the MNIST and OMNIGLOT datasets show that these r…
Monash University（莫纳什大学）；Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Many applications, such as text modelling, high-throughput sequencing, and recommender systems, require analysing sparse, high-dimensional, and overdispersed discrete (count-valued or binary) data. Although probabilistic matrix factorisation and linear/nonlinear latent factor models have enjoyed great success in modelling such data, many existing models may have inferior modelling performance due to the insufficient capability of modelling overdispersion in count-valued data and model misspecification in general. In this paper, we comprehensively study these issues and propose a variational au…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is faster and potentially more accurate than sampling. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributions on o…
Technion, IIT（以色列理工学院）；Meta AI Research（Meta人工智能研究院）
Discrete variational auto-encoders (VAEs) are able to represent semantic latent spaces in generative learning. In many real-life settings, the discrete latent space consists of high-dimensional structures, and propagating gradients through the relevant structures often requires enumerating over an exponentially large latent space. Recently, various approaches were devised to propagate approximated gradients without enumerating over the space of possible structures. In this work, we use Natural Evolution Strategies (NES), a class of gradient-free black-box optimization algorithms, to learn disc…
University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）
We show how to learn a neural topic model with discrete random variables---one that explicitly models each word's assigned topic---using neural variational inference that does not rely on stochastic backpropagation to handle the discrete variables. The model we utilize combines the expressive power of neural methods for representing sequences of text with the topic model's ability to capture global, thematic coherence. Using neural variational inference, we show improved perplexity and document understanding across multiple corpora. We examine the effect of prior parameters both on the model a…
The Chinese University of Hong Kong（香港中文大学）；Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））
Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last hidden state from the encoder is transformed to the latent space, which is insufficient to summarize data. The latter comes as a result of the imbalanced scale between the reconstruction loss and the KL divergence in the objective function. To tackle these issues, in this paper we propose the discrete variational attention model with categorical distribution o…
University at Buffalo（布法罗大学）；Criteo（Criteo公司）；Duke University（杜克大学）
Variational autoencoders (VAEs) are essential tools in end-to-end representation learning. However, the sequential text generation common pitfall with VAEs is that the model tends to ignore latent variables with a strong auto-regressive decoder. In this paper, we propose a principled approach to alleviate this issue by applying a discretized bottleneck to enforce an implicit latent feature matching in a more compact latent space. We impose a shared discrete latent space where each input is learned to choose a combination of latent atoms as a regularized latent representation. Our model endows …
Improved Variational Inference in Discrete VAEs using Error Correcting Codes
Dept. of Signal Theory and Communications, Universidad Rey Juan Carlos（信号理论与通信系，雷乌安卡洛斯大学）；Klipsch School of Electrical and Computer Engineering, New Mexico State University（电气与计算机工程学院，新墨西哥州立大学）；Instituto de Investigación Sanitaria Gregorio Marañón, Madrid, Spain（格里戈里奥·马兰农卫生研究所，马德里，西班牙）
Variational Autoencoder is a scalable method for learning latent variable models of complex data. It employs a clear objective that can be easily optimized. However, it does not explicitly measure the quality of learned representations. We propose a Variational Mutual Information Maximization Framework for VAE to address this issue. It provides an objective that maximizes the mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent code and allows one to select particular components of it to be most informative with …
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；The Chinese University of Hong Kong（香港中文大学）
Variational autoencoders (VAEs) have been widely applied for text modeling. In practice, however, they are troubled by two challenges: information underrepresentation and posterior collapse. The former arises as only the last hidden state of LSTM encoder is transformed into the latent space, which is generally insufficient to summarize the data. The latter is a long-standing problem during the training of VAEs as the optimization is trapped to a disastrous local optimum. In this paper, we propose Discrete Auto-regressive Variational Attention Model (DAVAM) to address the challenges. Specifical…
The University of Tokyo（东京大学）；Keio University（庆应义塾大学）；IBM Japan（IBM日本）
Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC), an important primitive to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum…
Ping An Technology (Shenzhen) Co., Ltd.（平安科技（深圳）有限公司）
Recently, the speaker clustering model based on aggregation hierarchy cluster (AHC) is a common method to solve two main problems: no preset category number clustering and fix category number clustering. In general, model takes features like i-vectors as input of probability and linear discriminant analysis model (PLDA) aims to form the distance matric in long voice application scenario, and then clustering results are obtained through the clustering model. However, traditional speaker clustering method based on AHC has the shortcomings of long-time running and remains sensitive to environment…
