Representation learning is a central challenge across a range of machine learning areas. In reinforcement learning, effective and functional representations have the potential to tremendously accelerate learning progress and solve more challenging problems. Most prior work on representation learning has focused on generative approaches, learning representations that capture all underlying factors of variation in the observation space in a more disentangled or well-ordered manner. In this paper, we instead aim to learn functionally salient representations: representations that are not necessarily complete in terms of capturing all factors of variation in the observation space, but rather aim to capture those factors of variation that are important for decision making -- that are "actionable." These representations are aware of the dynamics of the environment, and capture only the elements of the observation that are necessary for decision making rather than all factors of variation, without explicit reconstruction of the observation. We show how these representations can be useful to improve exploration for sparse reward problems, to enable long horizon hierarchical reinforcement learning, and as a state representation for learning policies for downstream tasks. We evaluate our method on a number of simulated environments, and compare it to prior methods for representation learning, exploration, and hierarchical reinforcement learning.

Generative Adversarial Nets (GANs) are emerging objects of study in machine learning, computer vision, natural language processing, and many other domains. In machine learning, study of such a framework has led to significant advances in adversarial defenses [28, 24] and machine security [4, 24]. In computer vision and natural language processing, GANs have resulted in improved performance over standard generative models for images and texts [13], such as variational autoencoder [16] and deep Boltzmann machine [22]. A main technique to achieve this goal is to play a minimax two-player game between generator and discriminator under the design that the generator tries to confuse the discriminator with its generated contents and the discriminator tries to distinguish real images/texts from what the generator creates. Despite a large amount of variants of GANs, many fundamental questions remain unresolved. One of the longstanding challenges is designing universal, easy-to-implement architectures that alleviate the instability issue of GANs training. Ideally, GANs are supposed to solve the minimax optimization problem [13], but in practice alternating gradient descent methods do not clearly privilege minimax over maximin or vice versa (page 35, [12]), which may lead to instability in training if there exists a large discrepancy between the minimax and maximin objective values. The focus of this work is on improving the stability of such minimax game in the training process of GANs. 1 Under review as a conference paper at ICLR 2019

The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The classic examples are the Fourier and wavelet transforms that enjoy numerically efficient implementations (FFT and FWT, respectively). Unfortunately, orthonormal transformations are in general unstructured, and therefore they do not enjoy low computational complexity properties. In this paper, based on Householder reflectors, we introduce a class of orthonormal matrices that are numerically efficient to manipulate: we control the complexity of matrix-vector multiplications with these matrices using a given parameter. We provide numerical algorithms that approximate any orthonormal or symmetric transform with a new orthonormal or symmetric structure made up of products of a given number of Householder reflectors. We show analyses and numerical evidence to highlight the accuracy of the proposed approximations and provide an application to the case of learning fast Mahanalobis distance metric transformations.

The success of deep networks in a range of prediction tasks has raised the question of whether they can serve as models for processing in the cortex [4, 8]. These networks are most successful when trained using versions of stochastic gradient descent, where small random subsets of training data are used to compute the gradient of the loss function with respect to the weights connecting subsequent layers and then update them. Due to the particular structure of the function represented by these multi-layer networks the 1 gradient is computed using back-propagation - an algorithmic formulation of the chain rule. In all but the last layer, the gradient of a weight in this algorithm is a product of the activity of the units it connects - the pre-synaptic input unit in the lower layer and the post-synaptic output unit in the higher layer. In that sense it is performing a form of local Hebbian learning: the update depends on the product of the feedback activity in the post-synaptic unit (the error signal) and the activity of the pre-synaptic unit.

Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently, SPOS avoids the particle-collapsing pitfall of SVGD. Nevertheless, variance reduction in SPOS has never been studied. In this paper, we bridge the gap by presenting several variance-reduction techniques for SPOS. Specifically, we propose three variants of variance-reduced SPOS, called SAGA particle-optimization sampling (SAGA-POS), SVRG particle-optimization sampling (SVRG-POS) and a variant of SVRG-POS which avoids full gradient computations, denoted as SVRG-POS$^+$. Importantly, we provide non-asymptotic convergence guarantees for these algorithms in terms of 2-Wasserstein metric and analyze their complexities. Remarkably, the results show our algorithms yield better convergence rates than existing variance-reduced variants of stochastic Langevin dynamics, even though more space is required to store the particles in training. Our theory well aligns with experimental results on both synthetic and real datasets.

Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by much when one person's data changes. In many applications such as hyperparameter optimization, this stability assumption is much too strong. In this work, we consider the selection problem under a much weaker stability assumption on the candidates, namely that the score functions are differentially private. Under this assumption, we present algorithms that are near-optimal along the three relevant dimensions: privacy, utility and computational efficiency. Our result can be seen as a generalization of the exponential mechanism and its existing generalizations. We also develop an online version of our algorithm, that can be seen as a generalization of the sparse vector technique to this weaker stability assumption. We show how our results imply better algorithms for hyperparameter selection in differentially private machine learning, as well as for adaptive data analysis.

Throughout this paper, we use lower case letters to denote scalars and vectors, and use upper case letters to denote random variablesand matrices. We consider the model change detection problem in the following setting. ABSTRACT Model change detection is studied, in which there are two sets of samples that are independently and identically distributed (i.i.d.) according to a pre-change probabilistic model with parameter θ,and a post-change model with parameter θ The goal is to detect whether the change in the model is significant, i.e., whether the difference between the prechange parameterand the post-change parameter ‖θ θ The problem is considered in a Neyman-Pearson setting, where the goal is to maximize the probability of detection under a false alarm constraint. Since the generalized likelihood ratio test (GLRT) is difficult to compute in this problem, we construct an empirical differencetest (EDT), which approximates the GLRT and has low computational complexity. Moreover, we provide an approximation method to set the threshold of the EDT to meet the false alarm constraint.

We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However, privacy guarantees cannot be evaluated empirically, and must be proven --- without making heuristic assumptions. We show that learning problems over broad classes of functions can be solved privately and efficiently, assuming the existence of a non-private oracle for solving the same problem. Our first algorithm yields a privacy guarantee that is contingent on the correctness of the oracle. We then give a reduction which applies to a class of heuristics which we call certifiable, which allows us to convert oracle-dependent privacy guarantees to worst-case privacy guarantee that hold even when the heuristic standing in for the oracle might fail in adversarial ways. Finally, we consider a broad class of functions that includes most classes of simple boolean functions studied in the PAC learning literature, including conjunctions, disjunctions, parities, and discrete halfspaces. We show that there is an efficient algorithm for privately constructing synthetic data for any such class, given a non-private learning oracle. This in particular gives the first oracle-efficient algorithm for privately generating synthetic data for contingency tables. The most intriguing question left open by our work is whether or not every problem that can be solved differentially privately can be privately solved with an oracle-efficient algorithm. While we do not resolve this, we give a barrier result that suggests that any generic oracle-efficient reduction must fall outside of a natural class of algorithms (which includes the algorithms given in this paper).

Data-driven fault diagnostics and prognostics suffers from class-imbalance problem in industrial systems and it raises challenges to common machine learning algorithms as it becomes difficult to learn the features of the minority class samples. Synthetic oversampling methods are commonly used to tackle these problems by generating the minority class samples to balance the distributions between majority and minority classes. However, many of oversampling methods are inappropriate that they cannot generate effective and useful minority class samples according to different distributions of data, which further complicate the process of learning samples. Thus, this paper proposes a novel adaptive oversampling technique: EM-based Weighted Minority Oversampling TEchnique (EWMOTE) for industrial fault diagnostics and prognostics. The methods comprises a weighted minority sampling strategy to identify hard-to-learn informative minority fault samples and Expectation Maximization (EM) based imputation algorithm to generate fault samples. To validate the performance of the proposed methods, experiments are conducted in two real datasets. The results show that the method could achieve better performance on not only binary class, but multi-class imbalance learning task in different imbalance ratios than other oversampling-based baseline models.

We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian distribution, which makes the model unsuited for data with e.g. categorical or nominal attributes. Our model, for which we use a sampling based variational inference, instead assumes a separate likelihood for each observed dimension. This formulation results in more meaningful latent representations, and give better predictive performance for real world data with dimensions of different types.