Recent state-of-the-art autoencoder based generative models have an encoder-decoder structure and learn a latent representation with a pre-defined distribution that can be sampled from. Implementing the encoder networks of these models in a stochastic manner provides a natural and common approach to avoid overfitting and enforce a smooth decoder function. However, we show that for stochastic encoders, simultaneously attempting to enforce a distribution constraint and minimising an output distortion leads to a reduction in generative and reconstruction quality. In addition, attempting to enforce a latent distribution constraint is not reasonable when performing disentanglement. Hence, we propose the variance-constrained autoencoder (VCAE), which only enforces a variance constraint on the latent distribution. Our experiments show that VCAE improves upon Wasserstein Autoencoder and the Variational Autoencoder in both reconstruction and generative quality on MNIST and CelebA. Moreover, we show that VCAE equipped with a total correlation penalty term performs equivalently to FactorVAE at learning disentangled representations on 3D-Shapes while being a more principled approach.
Conditional neural control variates for variance reduction in Bayesian inverse problems
Department of Computer Science University of Central Florida（计算机科学系佛罗里达中央大学）；Department of Physics and Maryland Center for Fundamental Physics University of Maryland College Park（物理系马里兰根本物理中心马里兰大学学院公园分校）
Xidian University（西安电子科技大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
To build a flexible and interpretable model for document analysis, we develop deep autoencoding topic model (DATM) that uses a hierarchy of gamma distributions to construct its multi-stochastic-layer generative network. In order to provide scalable posterior inference for the parameters of the generative network, we develop topic-layer-adaptive stochastic gradient Riemannian MCMC that jointly learns simplex-constrained global parameters across all layers and topics, with topic and layer specific learning rates. Given a posterior sample of the global parameters, in order to efficiently infer th…
We consider a linear autoencoder in which the latent variables are quantized, or corrupted by noise, and the constraint is Schur-concave in the set of latent variances. Although finding the optimal encoder/decoder pair for this setup is a nonconvex optimization problem, we show that decomposing the source into its principal components is optimal. If the constraint is strictly Schur-concave and the empirical covariance matrix has only simple eigenvalues, then any optimal encoder/decoder must decompose the source in this way. As one application, we consider a strictly Schur-concave constraint th…
Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression
Courant Institute School of Mathematics, Computing and Data Science（Courant学院数学、计算与数据科学系）
Imperial College London（帝国理工学院）；Facebook AI Applied Research（Facebook人工智能应用研究部）；University College London（伦敦大学学院）
Recent work in unsupervised learning has focused on efficient inference and learning in latent variables models. Training these models by maximizing the evidence (marginal likelihood) is typically intractable. Thus, a common approximation is to maximize the Evidence Lower BOund (ELBO) instead. Variational autoencoders (VAE) are a powerful and widely-used class of generative models that optimize the ELBO efficiently for large datasets. However, the VAE's default Gaussian choice for the prior imposes a strong constraint on its ability to represent the true posterior, thereby degrading overall pe…
University of Cambridge（剑桥大学）；Delft University of Technology（代尔夫特理工大学）
Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, which comes with no guarantee about deviations of particular output realizations around the optimal expectation. To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the stochastic deviation. An alternating primal-dual learning procedure is undertaken that solves the problem by updating the SGNN parameters with gradient des…
National University of Singapore（新加坡国立大学）；University of Alberta（阿尔伯塔大学）
We design and analyze VA-LUCB, a parameter-free algorithm, for identifying the best arm under the fixed-confidence setup and under a stringent constraint that the variance of the chosen arm is strictly smaller than a given threshold. An upper bound on VA-LUCB's sample complexity is shown to be characterized by a fundamental variance-aware hardness quantity $H_{VA}$. By proving a lower bound, we show that sample complexity of VA-LUCB is optimal up to a factor logarithmic in $H_{VA}$. Extensive experiments corroborate the dependence of the sample complexity on the various terms in $H_{VA}$. By c…
INRIA Lille - Nord Europe（法国国立信息学及其应用研究院里尔-北欧中心）；Adobe Research（奥多比研究院）；INRIA Lille（法国国立信息学及其应用研究院里尔中心）
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For ea…
Risk-Sensitive Deep RL: Variance-Constrained Actor-Critic Provably Finds Globally Optimal Policy
Northwestern University（西北大学）；Peking University（北京大学）；University of Science and Technology of China（中国科学技术大学）；Duke University（杜克大学）；Yale University（耶鲁大学）；Pennsylvania State University（宾夕法尼亚州立大学）
This work studies reinforcement learning (RL) in the context of multi-period supply chains subject to constraints, e.g., on production and inventory. We introduce Distributional Constrained Policy Optimization (DCPO), a novel approach for reliable constraint satisfaction in RL. Our approach is based on Constrained Policy Optimization (CPO), which is subject to approximation errors that in practice lead it to converge to infeasible policies. We address this issue by incorporating aspects of distributional RL into DCPO. Specifically, we represent the return and cost value functions using neural …
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of combinatorial problems, which involve a number of constraints that is polynomial in the problem dimension. The most important feature of our framework is that only a subset of the constraints is processed at each iteration, thus gaining a computational advantage over prior works that require full passes. Our algorithms rely on variance reduction and smoothing used in c…
Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures
University of Wrocław（弗罗茨瓦夫大学）；Tooploox；TRAILS；University of Warsaw（华沙大学）；Warsaw University of Technology（华沙理工大学）；IDEAS Research Institute（IDEAS研究所）；Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）
We evaluate two popular local explainability techniques, LIME and SHAP, on a movie recommendation task. We discover that the two methods behave very differently depending on the sparsity of the data set. LIME does better than SHAP in dense segments of the data set and SHAP does better in sparse segments. We trace this difference to the differing bias-variance characteristics of the underlying estimators of LIME and SHAP. We find that SHAP exhibits lower variance in sparse segments of the data compared to LIME. We attribute this lower variance to the completeness constraint property inherent in…
University of Pennsylvania（宾夕法尼亚大学）；University of Pittsburgh（匹兹堡大学）；Massachusetts Institute of Technology（麻省理工学院）
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to aid in the learning process for each individual domain. In this paper we draw intuition from the two extreme learning scenarios -- a single function for all tasks, and a task-specific function that ignores the other tasks dependencies -- to propose a bias-variance trade-off. To control the relationship between the variance (given by the number of i.i.d. sample…
The performance of federated learning systems is bottlenecked by communication costs and training variance. The communication overhead problem is usually addressed by three communication-reduction techniques, namely, model compression, partial device participation, and periodic aggregation, at the cost of increased training variance. Different from traditional distributed learning systems, federated learning suffers from data heterogeneity (since the devices sample their data from possibly different distributions), which induces additional variance among devices during training. Various varian…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；IBM Research（IBM研究院）；Michigan State University（密歇根州立大学）
Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In this paper, we design and analyze stochastic inexact augmented Lagrangian methods (Stoc-iALM) to solve problems involving a nonconvex composite (i.e. smooth+nonsmooth) objective and nonconvex smooth functional constraints. We adopt the standard iALM framework and design a subroutine by using the momentum-based variance-reduced proximal stochastic gradient me…
