NeurIPS 2018 论文列表

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 relaxations outperform previous discrete VAEs with Boltzmann priors. An implementation which reproduces these results is available.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: we formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree.

Stochastic regularisation is an important weapon in the arsenal of a deep learning practitioner. However, despite recent theoretical advances, our understanding of how noise influences signal propagation in deep neural networks remains limited. By extending recent work based on mean field theory, we develop a new framework for signal propagation in stochastic regularised neural networks. Our \textit{noisy signal propagation} theory can incorporate several common noise distributions, including additive and multiplicative Gaussian noise as well as dropout. We use this framework to investigate initialisation strategies for noisy ReLU networks. We show that no critical initialisation strategy exists using additive noise, with signal propagation exploding regardless of the selected noise distribution. For multiplicative noise (e.g.\ dropout), we identify alternative critical initialisation strategies that depend on the second moment of the noise distribution. Simulations and experiments on real-world data confirm that our proposed initialisation is able to stably propagate signals in deep networks, while using an initialisation disregarding noise fails to do so. Furthermore, we analyse correlation dynamics between inputs. Stronger noise regularisation is shown to reduce the depth to which discriminatory information about the inputs to a noisy ReLU network is able to propagate, even when initialised at criticality. We support our theoretical predictions for these trainable depths with simulations, as well as with experiments on MNIST and CIFAR-10.

Scaling decision theoretic planning to large multiagent systems is challenging due to uncertainty and partial observability in the environment. We focus on a multiagent planning model subclass, relevant to urban settings, where agent interactions are dependent on their ``collective influence'' on each other, rather than their identities. Unlike previous work, we address a general setting where system reward is not decomposable among agents. We develop collective actor-critic RL approaches for this setting, and address the problem of multiagent credit assignment, and computing low variance policy gradient estimates that result in faster convergence to high quality solutions. We also develop difference rewards based credit assignment methods for the collective setting. Empirically our new approaches provide significantly better solutions than previous methods in the presence of global rewards on two real world problems modeling taxi fleet optimization and multiagent patrolling, and a synthetic grid navigation domain.

Variational inference plays a vital role in learning graphical models, especially on large-scale datasets. Much of its success depends on a proper choice of auxiliary distribution class for posterior approximation. However, how to pursue an auxiliary distribution class that achieves both good approximation ability and computation efficiency remains a core challenge. In this paper, we proposed coupled variational Bayes which exploits the primal-dual view of the ELBO with the variational distribution class generated by an optimization procedure, which is termed optimization embedding. This flexible function class couples the variational distribution with the original parameters in the graphical models, allowing end-to-end learning of the graphical models by back-propagation through the variational distribution. Theoretically, we establish an interesting connection to gradient flow and demonstrate the extreme flexibility of this implicit distribution family in the limit sense. Empirically, we demonstrate the effectiveness of the proposed method on multiple graphical models with either continuous or discrete latent variables comparing to state-of-the-art methods.

Coordinate descent methods minimize a cost function by updating a single decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest marginal decrease in the cost function. However, finding this coordinate would require checking all of them, which is not computationally practical. Therefore, we propose a new adaptive method for coordinate descent. First, we define a lower bound on the decrease of the cost function when a coordinate is updated and, instead of calculating this lower bound for all coordinates, we use a multi-armed bandit algorithm to learn which coordinates result in the largest marginal decrease and simultaneously perform coordinate descent. We show that our approach improves the convergence of the coordinate methods both theoretically and experimentally.

We propose a new approach, called cooperative neural networks (CoNN), which use a set of cooperatively trained neural networks to capture latent representations that exploit prior given independence structure. The model is more flexible than traditional graphical models based on exponential family distributions, but incorporates more domain specific prior structure than traditional deep networks or variational autoencoders. The framework is very general and can be used to exploit the independence structure of any graphical model. We illustrate the technique by showing that we can transfer the independence structure of the popular Latent Dirichlet Allocation (LDA) model to a cooperative neural network, CoNN-sLDA. Empirical evaluation of CoNN-sLDA on supervised text classification tasks demonstrate that the theoretical advantages of prior independence structure can be realized in practice - we demonstrate a 23 percent reduction in error on the challenging MultiSent data set compared to state-of-the-art.

There is a natural correlation between the visual and auditive elements of a video. In this work we leverage this connection to learn general and effective models for both audio and video analysis from self-supervised temporal synchronization. We demonstrate that a calibrated curriculum learning scheme, a careful choice of negative examples, and the use of a contrastive loss are critical ingredients to obtain powerful multi-sensory representations from models optimized to discern temporal synchronization of audio-video pairs. Without further fine-tuning, the resulting audio features achieve performance superior or comparable to the state-of-the-art on established audio classification benchmarks (DCASE2014 and ESC-50). At the same time, our visual subnet provides a very effective initialization to improve the accuracy of video-based action recognition models: compared to learning from scratch, our self-supervised pretraining yields a remarkable gain of +19.9% in action recognition accuracy on UCF101 and a boost of +17.7% on HMDB51.

Holistic 3D indoor scene understanding refers to jointly recovering the i) object bounding boxes, ii) room layout, and iii) camera pose, all in 3D. The existing methods either are ineffective or only tackle the problem partially. In this paper, we propose an end-to-end model that simultaneously solves all three tasks in real-time given only a single RGB image. The essence of the proposed method is to improve the prediction by i) parametrizing the targets (e.g., 3D boxes) instead of directly estimating the targets, and ii) cooperative training across different modules in contrast to training these modules individually. Specifically, we parametrize the 3D object bounding boxes by the predictions from several modules, i.e., 3D camera pose and object attributes. The proposed method provides two major advantages: i) The parametrization helps maintain the consistency between the 2D image and the 3D world, thus largely reducing the prediction variances in 3D coordinates. ii) Constraints can be imposed on the parametrization to train different modules simultaneously. We call these constraints "cooperative losses" as they enable the joint training and inference. We employ three cooperative losses for 3D bounding boxes, 2D projections, and physical constraints to estimate a geometrically consistent and physically plausible 3D scene. Experiments on the SUN RGB-D dataset shows that the proposed method significantly outperforms prior approaches on 3D layout estimation, 3D object detection, 3D camera pose estimation, and holistic scene understanding.

A property or statistic of a distribution is said to be elicitable if it can be expressed as the minimizer of some loss function in expectation. Recent work shows that continuous real-valued properties are elicitable if and only if they are identifiable, meaning the set of distributions with the same property value can be described by linear constraints. From a practical standpoint, one may ask for which such properties do there exist convex loss functions. In this paper, in a finite-outcome setting, we show that in fact every elicitable real-valued property can be elicited by a convex loss function. Our proof is constructive, and leads to convex loss functions for new properties.

Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In this paper, we explore the asymptotic convergence rate of CR by exploiting the ubiquitous Kurdyka-Lojasiewicz (KL) property of the nonconvex objective functions. In specific, we characterize the asymptotic convergence rate of various types of optimality measures for CR including function value gap, variable distance gap, gradient norm and least eigenvalue of the Hessian matrix. Our results fully characterize the diverse convergence behaviors of these optimality measures in the full parameter regime of the KL property. Moreover, we show that the obtained asymptotic convergence rates of CR are order-wise faster than those of first-order gradient descent algorithms under the KL property.

Learning from pairwise measurements naturally arises from many applications, such as rank aggregation, ordinal embedding, and crowdsourcing. However, most existing models and algorithms are susceptible to potential model misspecification. In this paper, we study a semiparametric model where the pairwise measurements follow a natural exponential family distribution with an unknown base measure. Such a semiparametric model includes various popular parametric models, such as the Bradley-Terry-Luce model and the paired cardinal model, as special cases. To estimate this semiparametric model without specifying the base measure, we propose a data augmentation technique to create virtual examples, which enables us to define a contrastive estimator. In particular, we prove that such a contrastive estimator is invariant to model misspecification within the natural exponential family, and moreover, attains the optimal statistical rate of convergence up to a logarithmic factor. We provide numerical experiments to corroborate our theory.

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of mechanical and dynamical systems (reliability, probability of failure, stability, etc.). Our algorithm locates contours using information from multiple sources, which are available in the form of relatively inexpensive, biased, and possibly noisy approximations to the original function. Considering multiple information sources can lead to significant cost savings. We also introduce the concept of contour entropy, a formal measure of uncertainty about the location of the zero contour of a function approximated by a statistical surrogate model. Our algorithm locates contours efficiently by maximizing the reduction of contour entropy per unit cost.

Motivated by the success of reinforcement learning (RL) for discrete-time tasks such as AlphaGo and Atari games, there has been a recent surge of interest in using RL for continuous-time control of physical systems (cf. many challenging tasks in OpenAI Gym and DeepMind Control Suite). Since discretization of time is susceptible to error, it is methodologically more desirable to handle the system dynamics directly in continuous time. However, very few techniques exist for continuous-time RL and they lack flexibility in value function approximation. In this paper, we propose a novel framework for model-based continuous-time value function approximation in reproducing kernel Hilbert spaces. The resulting framework is so flexible that it can accommodate any kind of kernel-based approach, such as Gaussian processes and kernel adaptive filters, and it allows us to handle uncertainties and nonstationarity without prior knowledge about the environment or what basis functions to employ. We demonstrate the validity of the presented framework through experiments.

We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive a new margin-based regret bound in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an efficient algorithm with a $\sqrt{dT}$-type mistake bound against benchmark policies induced by $d$-dimensional regressors. Under realizability assumptions, our results also yield classical regret bounds.

We provide the first information theoretical tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same latent communities. Our work bridges recent theoretical breakthroughs in detection of latent community structure without nodes covariates and a large body of empirical work using diverse heuristics for combining node covariates with graphs for inference. The tightness of our analysis implies in particular, the information theoretic necessity of combining the different sources of information. Our analysis holds for networks of large degrees as well as for a Gaussian version of the model.

We investigate the problem of learning a Lipschitz function from binary feedback. In this problem, a learner is trying to learn a Lipschitz function $f:[0,1]^d \rightarrow [0,1]$ over the course of $T$ rounds. On round $t$, an adversary provides the learner with an input $x_t$, the learner submits a guess $y_t$ for $f(x_t)$, and learns whether $y_t > f(x_t)$ or $y_t \leq f(x_t)$. The learner's goal is to minimize their total loss $\sum_t\ell(f(x_t), y_t)$ (for some loss function $\ell$). The problem is motivated by \textit{contextual dynamic pricing}, where a firm must sell a stream of differentiated products to a collection of buyers with non-linear valuations for the items and observes only whether the item was sold or not at the posted price. For the symmetric loss $\ell(f(x_t), y_t) = \vert f(x_t) - y_t \vert$, we provide an algorithm for this problem achieving total loss $O(\log T)$ when $d=1$ and $O(T^{(d-1)/d})$ when $d>1$, and show that both bounds are tight (up to a factor of $\sqrt{\log T}$). For the pricing loss function $\ell(f(x_t), y_t) = f(x_t) - y_t {\bf 1}\{y_t \leq f(x_t)\}$ we show a regret bound of $O(T^{d/(d+1)})$ and show that this bound is tight. We present improved bounds in the special case of a population of linear buyers.

In this paper, we study the stochastic contextual combinatorial multi-armed bandit (CC-MAB) framework that is tailored for volatile arms and submodular reward functions. CC-MAB inherits properties from both contextual bandit and combinatorial bandit: it aims to select a set of arms in each round based on the side information (a.k.a. context) associated with the arms. By ``volatile arms'', we mean that the available arms to select from in each round may change; and by ``submodular rewards'', we mean that the total reward achieved by selected arms is not a simple sum of individual rewards but demonstrates a feature of diminishing returns determined by the relations between selected arms (e.g. relevance and redundancy). Volatile arms and submodular rewards are often seen in many real-world applications, e.g. recommender systems and crowdsourcing, in which multi-armed bandit (MAB) based strategies are extensively applied. Although there exist works that investigate these issues separately based on standard MAB, jointly considering all these issues in a single MAB problem requires very different algorithm design and regret analysis. Our algorithm CC-MAB provides an online decision-making policy in a contextual and combinatorial bandit setting and effectively addresses the issues raised by volatile arms and submodular reward functions. The proposed algorithm is proved to achieve $O(cT^{\frac{2\alpha+D}{3\alpha + D}}\log(T))$ regret after a span of $T$ rounds. The performance of CC-MAB is evaluated by experiments conducted on a real-world crowdsourcing dataset, and the result shows that our algorithm outperforms the prior art.

Directed exploration strategies for reinforcement learning are critical for learning an optimal policy in a minimal number of interactions with the environment. Many algorithms use optimism to direct exploration, either through visitation estimates or upper confidence bounds, as opposed to data-inefficient strategies like e-greedy that use random, undirected exploration. Most data-efficient exploration methods require significant computation, typically relying on a learned model to guide exploration. Least-squares methods have the potential to provide some of the data-efficiency benefits of model-based approaches—because they summarize past interactions—with the computation closer to that of model-free approaches. In this work, we provide a novel, computationally efficient, incremental exploration strategy, leveraging this property of least-squares temporal difference learning (LSTD). We derive upper confidence bounds on the action-values learned by LSTD, with context-dependent (or state-dependent) noise variance. Such context-dependent noise focuses exploration on a subset of variable states, and allows for reduced exploration in other states. We empirically demonstrate that our algorithm can converge more quickly than other incremental exploration strategies using confidence estimates on action-values.