In this paper, we propose a deep reinforcement learning (DRL) based mobility load balancing (MLB) algorithm along with a two-layer architecture to solve the large-scale load balancing problem for ultra-dense networks (UDNs). Our contribution is three-fold. First, this work proposes a two-layer architecture to solve the large-scale load balancing problem in a self-organized manner. The proposed architecture can alleviate the global traffic variations by dynamically grouping small cells into self-organized clusters according to their historical loads, and further adapt to local traffic variations through intra-cluster load balancing afterwards. Second, for the intra-cluster load balancing, this paper proposes an off-policy DRL-based MLB algorithm to autonomously learn the optimal MLB policy under an asynchronous parallel learning framework, without any prior knowledge assumed over the underlying UDN environments. Moreover, the algorithm enables joint exploration with multiple behavior policies, such that the traditional MLB methods can be used to guide the learning process thereby improving the learning efficiency and stability. Third, this work proposes an offline-evaluation based safeguard mechanism to ensure that the online system can always operate with the optimal and well-trained MLB policy, which not only stabilizes the online performance but also enables the exploration beyond current policies to make full use of machine learning in a safe way. Empirical results verify that the proposed framework outperforms the existing MLB methods in general UDN environments featured with irregular network topologies, coupled interferences, and random user movements, in terms of the load balancing performance.

This paper extends the proof of density of neural networks in the space of continuous (or even measurable) functions on Euclidean spaces to functions on compact sets of probability measures. By doing so the work parallels a more then a decade old results on mean-map embedding of probability measures in reproducing kernel Hilbert spaces. The work has wide practical consequences for multi-instance learning, where it theoretically justifies some recently proposed constructions. The result is then extended to Cartesian products, yielding universal approximation theorem for tree-structured domains, which naturally occur in data-exchange formats like JSON, XML, YAML, AVRO, and ProtoBuffer. This has important practical implications, as it enables to automatically create an architecture of neural networks for processing structured data (AutoML paradigms), as demonstrated by an accompanied library for JSON format.

We study the recently introduced stability training as a general-purpose method to increase the robustness of deep neural networks against input perturbations. In particular, we explore its use as an alternative to data augmentation and validate its performance against a number of distortion types and transformations including adversarial examples. In our ImageNet-scale image classification experiments stability training performs on a par or even outperforms data augmentation for specific transformations, while consistently offering improved robustness against a broader range of distortion strengths and types unseen during training, a considerably smaller hyperparameter dependence and less potentially negative side effects compared to data augmentation.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we can construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded, while exhibiting favourable latent representations on synthetic manifold data sets. Moreover, on real-world data sets, introducing our topological loss leads to more meaningful latent representations while preserving low reconstruction errors.

We investigate multiarmed bandits with delayed feedback, where the delays need neither be identical nor bounded. We first prove that the "delayed" Exp3 achieves the $O(\sqrt{(KT + D)\ln K})$ regret bound conjectured by Cesa-Bianchi et al. [2016], in the case of variable, but bounded delays. Here, $K$ is the number of actions and $D$ is the total delay over $T$ rounds. We then introduce a new algorithm that lifts the requirement of bounded delays by using a wrapper that skips rounds with excessively large delays. The new algorithm maintains the same regret bound, but similar to its predecessor requires prior knowledge of $D$ and $T$. For this algorithm we then construct a novel doubling scheme that forgoes this requirement under the assumption that the delays are available at action time (rather than at loss observation time). This assumption is satisfied in a broad range of applications, including interaction with servers and service providers. The resulting oracle regret bound is of order $\min_{\beta} (|S_\beta|+\beta \ln K + (KT + D_\beta)/\beta)$, where $|S_\beta|$ is the number of observations with delay exceeding $\beta$, and $D_\beta$ is the total delay of observations with delay below $\beta$. The bound relaxes to $O(\sqrt{(KT + D)\ln K})$, but we also provide examples where $D_\beta \ll D$ and the oracle bound has a polynomially better dependence on the problem parameters.

Continual learning consists in incrementally training a model on a sequence of datasets and testing on the union of all datasets. In this paper, we examine continual learning for the problem of sound classification, in which we wish to refine already trained models to learn new sound classes. In practice one does not want to maintain all past training data and retrain from scratch, but naively updating a model with new data(sets) results in a degradation of already learned tasks, which is referred to as "catastrophic forgetting." We develop a generative replay procedure for generating training audio spectrogram data, in place of keeping older training datasets. We show that by incrementally refining a classifier with generative replay a generator that is 4% of the size of all previous training data matches the performance of refining the classifier keeping 20% of all previous training data. We thus conclude that we can extend a trained sound classifier to learn new classes without having to keep previously used datasets.

We present an efficient technique, which allows to train classification networks which are verifiably robust against norm-bounded adversarial attacks. This framework is built upon the work of Gowal et al., who applies the interval arithmetic to bound the activations at each layer and keeps the prediction invariant to the input perturbation. While that method is faster than competitive approaches, it requires careful tuning of hyper-parameters and a large number of epochs to converge. To speed up and stabilize training, we supply the cost function with an additional term, which encourages the model to keep the interval bounds at hidden layers small. Experimental results demonstrate that we can achieve comparable (or even better) results using a smaller number of training iterations, in a more stable fashion. Moreover, the proposed model is not so sensitive to the exact specification of the training process, which makes it easier to use by practitioners.

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem to additive $\epsilon$ with $\tilde{O}(1/\epsilon)$ parallel depth, and $\tilde{O}\left(n^2/\epsilon\right)$ work. Barring a breakthrough on a long-standing algorithmic open problem, this is optimal for first-order methods. Blanchet et. al. '18, Quanrud '19 obtained similar runtimes through reductions to positive linear programming and matrix scaling. However, these reduction-based algorithms use complicated subroutines which may be deemed impractical due to requiring solvers for second-order iterations (matrix scaling) or non-parallelizability (positive LP). The fastest practical algorithms run in time $\tilde{O}(\min(n^2 / \epsilon^2, n^{2.5} / \epsilon))$ (Dvurechensky et. al. '18, Lin et. al. '19). We bridge this gap by providing a parallel, first-order, $\tilde{O}(1/\epsilon)$ iteration algorithm without worse dependence on dimension, and provide preliminary experimental evidence that our algorithm may enjoy improved practical performance. We obtain this runtime via a primal-dual extragradient method, motivated by recent theoretical improvements to maximum flow (Sherman '17).

In the coming years, the satellite broadband market will experience significant increases in the service demand, especially for the mobility sector, where demand is burstier. Many of the next generation of satellites will be equipped with numerous degrees of freedom in power and bandwidth allocation capabilities, making manual resource allocation impractical and inefficient. Therefore, it is desirable to automate the operation of these highly flexible satellites. This paper presents a novel power allocation approach based on Deep Reinforcement Learning (DRL) that represents the problem as continuous state and action spaces. We make use of the Proximal Policy Optimization (PPO) algorithm to optimize the allocation policy for minimum Unmet System Demand (USD) and power consumption. The performance of the algorithm is analyzed through simulations of a multibeam satellite system, which show promising results for DRL to be used as a dynamic resource allocation algorithm.

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found to provide improved clustering performance over the K-means. Solving the ONMF model is a challenging optimization problem due to the existence of both orthogonality and nonnegativity constraints, and most of the existing methods directly deal with the orthogonality constraint in its original form via various optimization techniques. In this paper, we propose a new ONMF based clustering formulation that equivalently transforms the orthogonality constraint into a set of norm-based non-convex equality constraints. We then apply a non-convex penalty (NCP) approach to add the non-convex equality constraints to the objective as penalty terms, leaving simple non-negativity constraints only in the penalized problem. One smooth penalty formulation and one non-smooth penalty formulation are respectively studied, and theoretical conditions for the penalized problems to provide feasible stationary solutions to the ONMF based clustering problem are presented. Experimental results based on both synthetic and real datasets are presented to show that the proposed NCP methods are computationally time efficient, and either match or outperform the existing K-means and ONMF based methods in terms of the clustering performance.