We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconvexity and nonconcavity, zero-sum LQ games have the property that the stationary point of the objective with respect to the feedback control policies constitutes the NE of the game. Building upon this, we develop three projected nested-gradient methods that are guaranteed to converge to the NE of the game. Moreover, we show that all of these algorithms enjoy both global sublinear and local linear convergence rates. Simulation results are then provided to validate the proposed algorithms. To the best of our knowledge, this work appears the first to investigate the optimization landscape of LQ games, and provably show the convergence of policy optimization methods to the Nash equilibria. Our work serves as an initial step of understanding the theoretical aspects of policy-based reinforcement learning algorithms for zero-sum Markov games in general.

Automatic estimation of relative difficulty of a pair of questions is an important and challenging problem in community question answering (CQA) services. There are limited studies which addressed this problem. Past studies mostly leveraged expertise of users answering the questions and barely considered other properties of CQA services such as metadata of users and posts, temporal information and textual content. In this paper, we propose DiffQue, a novel system that maps this problem to a network-aided edge directionality prediction problem. DiffQue starts by constructing a novel network structure that captures different notions of difficulties among a pair of questions. It then measures the relative difficulty of two questions by predicting the direction of a (virtual) edge connecting these two questions in the network. It leverages features extracted from the network structure, metadata of users/posts and textual description of questions and answers. Experiments on datasets obtained from two CQA sites (further divided into four datasets) with human annotated ground-truth show that DiffQue outperforms four state-of-the-art methods by a significant margin (28.77% higher F1 score and 28.72% higher AUC than the best baseline). As opposed to the other baselines, (i) DiffQue appropriately responds to the training noise, (ii) DiffQue is capable of adapting multiple domains (CQA datasets), and (iii) DiffQue can efficiently handle 'cold start' problem which may arise due to the lack of information for newly posted questions or newly arrived users.

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph structure (relation) does not necessarily reflect the true dependency and genuine relation may be missing due to the incomplete connections in the data. Furthermore, existing methods are ineffective to capture the temporal trends as the RNNs or CNNs employed in these methods cannot capture long-range temporal sequences. To overcome these limitations, we propose in this paper a novel graph neural network architecture, Graph WaveNet, for spatial-temporal graph modeling. By developing a novel adaptive dependency matrix and learn it through node embedding, our model can precisely capture the hidden spatial dependency in the data. With a stacked dilated 1D convolution component whose receptive field grows exponentially as the number of layers increases, Graph WaveNet is able to handle very long sequences. These two components are integrated seamlessly in a unified framework and the whole framework is learned in an end-to-end manner. Experimental results on two public traffic network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of our algorithm.

Recently, a method [7] was proposed to generate contrastive explanations for differentiable models such as deep neural networks, where one has complete access to the model. In this work, we propose a method, Model Agnostic Contrastive Explanations Method (MACEM), to generate contrastive explanations for \emph{any} classification model where one is able to \emph{only} query the class probabilities for a desired input. This allows us to generate contrastive explanations for not only neural networks, but models such as random forests, boosted trees and even arbitrary ensembles that are still amongst the state-of-the-art when learning on structured data [13]. Moreover, to obtain meaningful explanations we propose a principled approach to handle real and categorical features leading to novel formulations for computing pertinent positives and negatives that form the essence of a contrastive explanation. A detailed treatment of the different data types of this nature was not performed in the previous work, which assumed all features to be positive real valued with zero being indicative of the least interesting value. We part with this strong implicit assumption and generalize these methods so as to be applicable across a much wider range of problem settings. We quantitatively and qualitatively validate our approach over 5 public datasets covering diverse domains.

Various health-care applications such as assisted living, fall detection etc., require modeling of user behavior through Human Activity Recognition (HAR). HAR using mobile- and wearable-based deep learning algorithms have been on the rise owing to the advancements in pervasive computing. However, there are two other challenges that need to be addressed: first, the deep learning model should support on-device incremental training (model updation) from real-time incoming data points to learn user behavior over time, while also being resource-friendly; second, a suitable ground truthing technique (like Active Learning) should help establish labels on-the-fly while also selecting only the most informative data points to query from an oracle. Hence, in this paper, we propose ActiveHARNet, a resource-efficient deep ensembled model which supports on-device Incremental Learning and inference, with capabilities to represent model uncertainties through approximations in Bayesian Neural Networks using dropout. This is combined with suitable acquisition functions for active learning. Empirical results on two publicly available wrist-worn HAR and fall detection datasets indicate that ActiveHARNet achieves considerable efficiency boost during inference across different users, with a substantially low number of acquired pool points (at least 60% reduction) during incremental learning on both datasets experimented with various acquisition functions, thus demonstrating deployment and Incremental Learning feasibility.

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. If the problem has a statistical maximum likelihood formulation, a local test of global optimality can be constructed. In this paper, we develop an improved test, based on a global maximum validation function proposed by Biernacki, under the assumption that the statistical distribution is in the generalized location family, a condition often satisfied in imaging problems. In addition, a new reparameterization and embedding procedure is presented that exploits knowledge about the forward operator to improve the global maximum validation function. Finally, the reparameterized embedding technique is applied to a physically-motivated joint-inverse problem arising in camera blur estimation. The advantages of the proposed global optimum testing techniques are numerically demonstrated in terms of increased detection accuracy and reduced computation.

Recent years have seen a surge of interest in the problem of fair classification, which is concerned with disparities in classification output or performance when conditioned on a protected attribute such as race or gender, or ethnicity. Many measures of fairness have been introduced [1-14] and fairness-enhancing interventions have been proposed to mitigate these disparities [15]. Roughly categorized, these interventions either (i) change data used to train a classifier (pre-processing) [16-20], (ii) change a classifier's output (post-processing) [4, 21-24], or (iii) directly change a classification model to ensure fairness (in-processing) [5, 25-32]. This paper places more emphasis on probabilistic classification in which the outputs of interest are predicted probabilities of belonging to one of the classes, often referred to as scores, as opposed to binary predictions. Scores are desirable because they indicate confidences in predictions. We propose an optimization formulation for transforming scores to satisfy fairness constraints while minimizing the loss in utility. The formulation accommodates any fairness criteria that can be expressed as linear inequalities involving conditional means of scores, including variants of statistical parity (SP) [1] and equalized odds (EO) [4, 5]. We derive a closed-form expression for the optimal transformed scores and a convex dual optimization problem for the Lagrange multipliers that parametrize the transformation.

In this article, we investigate a family of classification algorithms defined by the principle of empirical risk minimization, in the high dimensional regime where the feature dimension $p$ and data number $n$ are both large and comparable. Based on recent advances in high dimensional statistics and random matrix theory, we provide under mixture data model a unified stochastic characterization of classifiers learned with different loss functions. Our results are instrumental to an in-depth understanding as well as practical improvements on this fundamental classification approach. As the main outcome, we demonstrate the existence of a universally optimal loss function which yields the best high dimensional performance at any given $n/p$ ratio.

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of models. An attractive feature of these models is that they can admit analytic predictive means even when the likelihood is non-linear and the predictive distributions are non-Gaussian. We validate the modeling potential of these models in a variety of experiments in both the supervised and unsupervised setting. We demonstrate that the flexibility of these `neural' likelihoods can improve prediction quality as compared to simpler Gaussian process models and that neural likelihoods can be readily combined with a variety of underlying Gaussian process models, including deep Gaussian processes.

Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an unobserved sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing more than 12 600 trained representations of state-of-the-art disentangled models, we observe that various disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.