Deep generative models play an increasingly important role in machine learning and computer vision. However there are two fundamental issues hindering real-world applications of these techniques: the learning difficulty of variational inference in Variational AutoEncoder (VAE) and the functional absence of encoding samples in Generative Adversarial Network (GAN). In this paper, we manage to address these issues in one framework by proposing a novel algorithm named Latently Invertible Autoencoder (LIA). A deep invertible network and its inverse mapping are symmetrically embedded in the latent space of VAE. Thus the partial encoder first transforms inputs to be feature vectors and then the distribution of these feature vectors is reshaped to approach a prior by the invertible network. The decoder proceeds in reverse order of composite mappings of the complete encoder. The two-stage stochasticity-free training is devised to train LIA via adversarial learning, in the sense that we first train a standard GAN whose generator is the decoder of LIA and then an autoencoder in the adversarial manner by detaching the invertible network from LIA. Experiments conducted on the FFHQ dataset validate the effectiveness of LIA for inference and generation tasks.

We propose behavior-driven optimization via Wasserstein distances (WDs) to improve several classes of state-of-the-art reinforcement learning (RL) algorithms. We show that WD regularizers acting on appropriate policy embeddings efficiently incorporate behavioral characteristics into policy optimization. We demonstrate that they improve Evolution Strategy methods by encouraging more efficient exploration, can be applied in imitation learning and to speed up training of Trust Region Policy Optimization methods. Since the exact computation of WDs is expensive, we develop approximate algorithms based on the combination of different methods: dual formulation of the optimal transport problem, alternating optimization and random feature maps, to effectively replace exact WD computations in the RL tasks considered. We provide theoretical analysis of our algorithms and exhaustive empirical evaluation in a variety of RL settings.

Two distinct limits for deep learning as the net width $h\to\infty$ have been proposed, depending on how the weights of the last layer scale with $h$. In the "lazy-learning" regime, the dynamics becomes linear in the weights and is described by a Neural Tangent Kernel $\Theta$. By contrast, in the "feature-learning" regime, the dynamics can be expressed in terms of the density distribution of the weights. Understanding which regime describes accurately practical architectures and which one leads to better performance remains a challenge. We answer these questions and produce new characterizations of these regimes for the MNIST data set, by considering deep nets $f$ whose last layer of weights scales as $\frac{\alpha}{\sqrt{h}}$ at initialization, where $\alpha$ is a parameter we vary. We performed systematic experiments on two setups (A) fully-connected Softplus momentum full batch and (B) convolutional ReLU momentum stochastic. We find that (1) $\alpha^*=\frac{1}{\sqrt{h}}$ separates the two regimes. (2) for (A) and (B) feature learning outperforms lazy learning, a difference in performance that decreases with $h$ and becomes hardly detectable asymptotically for (A) but is very significant for (B). (3) In both regimes, the fluctuations $\delta f$ induced by initial conditions on the learned function follow $\delta f\sim1/\sqrt{h}$, leading to a performance that increases with $h$. This improvement can be instead obtained at intermediate $h$ values by ensemble averaging different networks. (4) In the feature regime there exists a time scale $t_1\sim\alpha\sqrt{h}$, such that for $t\ll t_1$ the dynamics is linear. At $t\sim t_1$, the output has grown by a magnitude $\sqrt{h}$ and the changes of the tangent kernel $\|\Delta\Theta\|$ become significant. Ultimately, it follows $\|\Delta\Theta\|\sim(\sqrt{h}\alpha)^{-a}$ for ReLU and Softplus activation, with $a<2$ & $a\to2$ when depth grows.

Explainability in Artificial Intelligence has been revived as a topic of active research by the need of conveying safety and trust to users in the `how' and `why' of automated decision-making. Whilst a plethora of approaches have been developed for post-hoc explainability, only a few focus on how to use domain knowledge, and how this influences the understandability of an explanation from the users' perspective. In this paper we show how ontologies help the understandability of interpretable machine learning models, such as decision trees. In particular, we build on Trepan, an algorithm that explains artificial neural networks by means of decision trees, and we extend it to include ontologies modeling domain knowledge in the process of generating explanations. We present the results of a user study that measures the understandability of decision trees in domains where explanations are critical, namely, in finance and medicine. Our study shows that decision trees taking into account domain knowledge during generation are more understandable than those generated without the use of ontologies.

Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper gives bounds for the common "reparameterization" estimators when the target is smooth and the variational family is a location-scale distribution. These bounds are unimprovable and thus provide the best possible guarantees under the stated assumptions.

State representation learning, or the ability to capture latent generative factors of an environment, is crucial for building intelligent agents that can perform a wide variety of tasks. Learning such representations without supervision from rewards is a challenging open problem. We introduce a method that learns state representations by maximizing mutual information across spatially and temporally distinct features of a neural encoder of the observations. We also introduce a new benchmark based on Atari 2600 games where we evaluate representations based on how well they capture the ground truth state variables. We believe this new framework for evaluating representation learning models will be crucial for future representation learning research. Finally, we compare our technique with other state-of-the-art generative and contrastive representation learning methods.

We consider a class of restless multi-armed bandit (RMAB) problems with unknown arm dynamics. At each time, a player chooses an arm out of N arms to play, referred to as an active arm, and receives a random reward from a finite set of reward states. The reward state of the active arm transits according to an unknown Markovian dynamics. The reward state of passive arms (which are not chosen to play at time t) evolves according to an arbitrary unknown random process. The objective is an arm-selection policy that minimizes the regret, defined as the reward loss with respect to a player that always plays the most rewarding arm. This class of RMAB problems has been studied recently in the context of communication networks and financial investment applications. We develop a strategy that selects arms to be played in a consecutive manner, dubbed Adaptive Sequencing Rules (ASR) algorithm. The sequencing rules for selecting arms under the ASR algorithm are adaptively updated and controlled by the current sample reward means. By designing judiciously the adaptive sequencing rules, we show that the ASR algorithm achieves a logarithmic regret order with time, and a finite-sample bound on the regret is established. Although existing methods have shown a logarithmic regret order with time in this RMAB setting, the theoretical analysis shows a significant improvement in the regret scaling with respect to the system parameters under ASR. Extensive simulation results support the theoretical study and demonstrate strong performance of the algorithm as compared to existing methods.

Imitation Learning describes the problem of recovering an expert policy from demonstrations. While inverse reinforcement learning approaches are known to be very sample-efficient in terms of expert demonstrations, they usually require problem-dependent reward functions or a (task-)specific reward-function regularization. In this paper, we show a natural connection between inverse reinforcement learning approaches and Optimal Transport, that enables more general reward functions with desirable properties (e.g., smoothness). Based on our observation, we propose a novel approach called Wasserstein Adversarial Imitation Learning. Our approach considers the Kantorovich potentials as a reward function and further leverages regularized optimal transport to enable large-scale applications. In several robotic experiments, our approach outperforms the baselines in terms of average cumulative rewards and shows a significant improvement in sample-efficiency, by requiring just one expert demonstration.

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size $k$ and desired accuracy $\varepsilon$: $\textbf{Distribution estimation}$ Under $\ell_1$ distance, PML yields optimal $\Theta(k/(\varepsilon^2\log k))$ sample complexity for sorted-distribution estimation, and a PML-based estimator empirically outperforms the Good-Turing estimator on the actual distribution; $\textbf{Additive property estimation}$ For a broad class of additive properties, the PML plug-in estimator uses just four times the sample size required by the best estimator to achieve roughly twice its error, with exponentially higher confidence; $\boldsymbol{\alpha}\textbf{-R\'enyi entropy estimation}$ For integer $\alpha>1$, the PML plug-in estimator has optimal $k^{1-1/\alpha}$ sample complexity; for non-integer $\alpha>3/4$, the PML plug-in estimator has sample complexity lower than the state of the art; $\textbf{Identity testing}$ In testing whether an unknown distribution is equal to or at least $\varepsilon$ far from a given distribution in $\ell_1$ distance, a PML-based tester achieves the optimal sample complexity up to logarithmic factors of $k$. With minor modifications, most of these results also hold for a near-linear-time computable variant of PML.

Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be manipulated arbitrarily by applying visually hardly perceptible perturbations to the input that keep the network's output approximately constant. We establish theoretically that this phenomenon can be related to certain geometrical properties of neural networks. This allows us to derive an upper bound on the susceptibility of explanations to manipulations. Based on this result, we propose effective mechanisms to enhance the robustness of explanations.