We introduce the lookahead-bounded Q-learning (LBQL) algorithm, a new, provably convergent variant of Q-learning that seeks to improve the performance of standard Q-learning in stochastic environments through the use of ``lookahead'' upper and lower bounds. To do this, LBQL employs previously collected experience and each iteration's state-action values as dual feasible penalties to construct a sequence of sampled information relaxation problems. The solutions to these problems provide estimated upper and lower bounds on the optimal value, which we track via stochastic approximation. These quantities are then used to constrain the iterates to stay within the bounds at every iteration. Numerical experiments on benchmark problems show that LBQL exhibits faster convergence and more robustness to hyperparameters when compared to standard Q-learning and several related techniques. Our approach is particularly appealing in problems that require expensive simulations or real-world interactions.

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine learning predictions. In many real-world cases, it is of utmost importance to estimate the capabilities of a machine learning algorithm to generalize, i.e., to provide accurate predictions on unseen data, depending on the characteristics of the target problem. In this work, we perform a meta-analysis of 109 publicly-available classification data sets, modeling machine learning generalization as a function of a variety of data set characteristics, ranging from number of samples to intrinsic dimensionality, from class-wise feature skewness to $F1$ evaluated on test samples falling outside the convex hull of the training set. Experimental results demonstrate the relevance of using the concept of the convex hull of the training data in assessing machine learning generalization, by emphasizing the difference between interpolated and extrapolated predictions. Besides several predictable correlations, we observe unexpectedly weak associations between the generalization ability of machine learning models and all metrics related to dimensionality, thus challenging the common assumption that the \textit{curse of dimensionality} might impair generalization in machine learning.

We propose a new algorithm for the $k$-means problem which repeatedly increases and decreases the number of centroids by $m$ in order to find an approximate solution. New centroids are inserted in areas where they will likely reduce the error. The subsequent removal of centroids is done such that the resulting raise in error is small. After each increase or decrease step standard $k$-means is performed. Termination is guaranteed by decrementing $m$ after each increase/decrease cycle unless the overall error was lowered. In experiments with Gaussian mixture distributions the new algorithm produced on average solutions several percent better than $k$-means++.

Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power of these GNN architectures. The current universality theorems only apply to intractable classes of GNNs. Here, we prove the first approximation guarantees for practical GNNs, paving the way for a better understanding of their generalization. Our theoretical results are proved for invariant GNNs computing a graph embedding (permutation of the nodes of the input graph does not affect the output) and equivariant GNNs computing an embedding of the nodes (permutation of the input permutes the output). We show that Folklore Graph Neural Networks (FGNN), which are tensor based GNNs augmented with matrix multiplication are the most expressive architectures proposed so far for a given tensor order. We illustrate our results on the Quadratic Assignment Problem (a NP-Hard combinatorial problem) by showing that FGNNs are able to learn how to solve the problem, leading to much better average performances than existing algorithms (based on spectral, SDP or other GNNs architectures). On a practical side, we also implement masked tensors to handle batches of graphs of varying sizes.

Along with the proliferation of Artificial Intelligence (AI) and Internet of Things (IoT) techniques, various kinds of adversarial attacks are increasingly emerging to fool Deep Neural Networks (DNNs) used by Industrial IoT (IIoT) applications. Due to biased training data or vulnerable underlying models, imperceptible modifications on inputs made by adversarial attacks may result in devastating consequences. Although existing methods are promising in defending such malicious attacks, most of them can only deal with limited existing attack types, which makes the deployment of large-scale IIoT devices a great challenge. To address this problem, we present an effective federated defense approach named FDA3 that can aggregate defense knowledge against adversarial examples from different sources. Inspired by federated learning, our proposed cloud-based architecture enables the sharing of defense capabilities against different attacks among IIoT devices. Comprehensive experimental results show that the generated DNNs by our approach can not only resist more malicious attacks than existing attack-specific adversarial training methods, but also can prevent IIoT applications from new attacks.

Sparsity has become popular in machine learning, because it can save computational resources, facilitate interpretations, and prevent overfitting. In this paper, we discuss sparsity in the framework of neural networks. In particular, we formulate a new notion of sparsity that concerns the networks' layers and, therefore, aligns particularly well with the current trend toward deep networks. We call this notion layer sparsity. We then introduce corresponding regularization and refitting schemes that can complement standard deep-learning pipelines to generate more compact and accurate networks.

We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph over a homogeneous metric space where the probability of two vertices to be connected is an arbitrary function of the distance. We give sufficient conditions under which the locations can be recovered (up to an isomorphism of the space) in the sparse regime. Moreover, we define a geometric counterpart of the model of flow of information on trees, due to Mossel and Peres, in which one considers a branching random walk on a sphere and the goal is to recover the location of the root based on the locations of leaves. We give some sufficient conditions for percolation and for non-percolation of information in this model.

This has made it easier to step outside the rigid model and approximation families designed based on computational tractability, and to switch to flexible distributions parameterized by neural networks, including normalizing flows relying on invertible transformation of simple base distributions [21]. Models with discrete latent variables, however, remain problematic due to non-differentiability of the sampling operation that prevents efficient optimization of expectations over the approximation. Hence in practice, we still largely resort to model-specific algorithms that are tedious to extend already for minor variants of the model, analytic marginalization of the discrete latent variables (e.g., mixture models and LDA in Stan [7]), continuous relaxations like the concrete distribution [19, 13], or (semi-)implicit approximations that do not support probability evaluation [34, 30]. Normalizing flows [25, 15, 21], suitable for learning flexible posterior approximations for continuous variables, have recently been generalized also for discrete categorical [31] and ordinal [12] variables. However, the discrete variants have only been applied in generative modeling of discrete observations. Even though discrete normalizing flows for categorical distributions (DNF) retain the property of differentiable Monte Carlo estimates, they are not very suitable for variational approximation due to their limited expressive power. As we will show later, a DNF can only move probability mass around and hence relies extremely strongly on use of base distributions that are already expressive (and of the same dimension as the final distribution). For generative modeling this can be satisfied, for example by using recurrent neural networks as base distributions in the case of language modeling [31], but for modeling latent variables there are no easy ways of learning strong base distributions. We improve the expressive power of DNFs by constructing mixtures of categorical discrete normalizing flows (MDNF).

Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover the latent vector that generated it. Building upon sparse representation theory, we define conditions that are applicable to any inversion algorithm (gradient descent, deep encoder, etc.), under which such generative models are invertible with a unique solution. Importantly, the proposed analysis is applicable to any trained model, and does not depend on Gaussian i.i.d. weights. Furthermore, we introduce two layer-wise inversion pursuit algorithms for trained generative networks of arbitrary depth, and accompany these with recovery guarantees. Finally, we validate our theoretical results numerically and show that our method outperforms gradient descent when inverting such generators, both for clean and corrupted signals.

In this paper, we propose a confidence-calibration method for predicting the winner of a famous multiplayer online battle arena (MOBA) game, League of Legends. In MOBA games, the dataset may contain a large amount of input-dependent noise; not all of such noise is observable. Hence, it is desirable to attempt a confidence-calibrated prediction. Unfortunately, most existing confidence calibration methods are pertaining to image and document classification tasks where consideration on uncertainty is not crucial. In this paper, we propose a novel calibration method that takes data uncertainty into consideration. The proposed method achieves an outstanding expected calibration error (ECE) (0.57%) mainly owing to data uncertainty consideration, compared to a conventional temperature scaling method of which ECE value is 1.11%.