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General policy improvement (GPI) and trust-region learning (TRL) are the predominant frameworks within contemporary reinforcement learning (RL), which serve as the core models for solving Markov decision processes (MDPs). Unfortunately, in their mathematical form, they are sensitive to modifications, and thus, the practical instantiations that implement them do not automatically inherit their improvement guarantees. As a result, the spectrum of available rigorous MDP-solvers is narrow. Indeed, many state-of-the-art (SOTA) algorithms, such as TRPO and PPO, are not proven to converge. In this paper, we propose \textsl{mirror learning} -- a general solution to the RL problem. We reveal GPI and TRL to be but small points within this far greater space of algorithms which boasts the monotonic improvement property and converges to the optimal policy. We show that virtually all SOTA algorithms for RL are instances of mirror learning, and thus suggest that their empirical performance is a consequence of their theoretical properties, rather than of approximate analogies. Excitingly, we show that mirror learning opens up a whole new space of policy learning methods with convergence guarantees.

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, is simpler to implement. It solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

Stochastic majorization-minimization (SMM) is an online extension of the classical principle of majorization-minimization, which consists of sampling i.i.d. data points from a fixed data distribution and minimizing a recursively defined majorizing surrogate of an objective function. In this paper, we introduce stochastic block majorization-minimization, where the surrogates can now be only block multi-convex and a single block is optimized at a time within a diminishing radius. Relaxing the standard strong convexity requirements for surrogates in SMM, our framework gives wider applicability including online CANDECOMP/PARAFAC (CP) dictionary learning and yields greater computational efficiency especially when the problem dimension is large. We provide an extensive convergence analysis on the proposed algorithm, which we derive under possibly dependent data streams, relaxing the standard i.i.d. assumption on data samples. We show that the proposed algorithm converges almost surely to the set of stationary points of a nonconvex objective under constraints at a rate $O((\log n)^{1+\eps}/n^{1/2})$ for the empirical loss function and $O((\log n)^{1+\eps}/n^{1/4})$ for the expected loss function, where $n$ denotes the number of data samples processed. Under some additional assumption, the latter convergence rate can be improved to $O((\log n)^{1+\eps}/n^{1/2})$. Our results provide first convergence rate bounds for various online matrix and tensor decomposition algorithms under a general Markovian data setting.

Tagging based relational triple extraction methods are attracting growing research attention recently. However, most of these methods take a unidirectional extraction framework that first extracts all subjects and then extracts objects and relations simultaneously based on the subjects extracted. This framework has an obvious deficiency that it is too sensitive to the extraction results of subjects. To overcome this deficiency, we propose a bidirectional extraction framework based method that extracts triples based on the entity pairs extracted from two complementary directions. Concretely, we first extract all possible subject-object pairs from two paralleled directions. These two extraction directions are connected by a shared encoder component, thus the extraction features from one direction can flow to another direction and vice versa. By this way, the extractions of two directions can boost and complement each other. Next, we assign all possible relations for each entity pair by a biaffine model. During training, we observe that the share structure will lead to a convergence rate inconsistency issue which is harmful to performance. So we propose a share-aware learning mechanism to address it. We evaluate the proposed model on multiple benchmark datasets. Extensive experimental results show that the proposed model is very effective and it achieves state-of-the-art results on all of these datasets. Moreover, experiments show that both the proposed bidirectional extraction framework and the share-aware learning mechanism have good adaptability and can be used to improve the performance of other tagging based methods. The source code of our work is available at: //github.com/neukg/BiRTE.

Learning low-dimensional representations for entities and relations in knowledge graphs using contrastive estimation represents a scalable and effective method for inferring connectivity patterns. A crucial aspect of contrastive learning approaches is the choice of corruption distribution that generates hard negative samples, which force the embedding model to learn discriminative representations and find critical characteristics of observed data. While earlier methods either employ too simple corruption distributions, i.e. uniform, yielding easy uninformative negatives or sophisticated adversarial distributions with challenging optimization schemes, they do not explicitly incorporate known graph structure resulting in suboptimal negatives. In this paper, we propose Structure Aware Negative Sampling (SANS), an inexpensive negative sampling strategy that utilizes the rich graph structure by selecting negative samples from a node's k-hop neighborhood. Empirically, we demonstrate that SANS finds high-quality negatives that are highly competitive with SOTA methods, and requires no additional parameters nor difficult adversarial optimization.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16].

Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

Knowledge Graph (KG) embedding is a fundamental problem in data mining research with many real-world applications. It aims to encode the entities and relations in the graph into low dimensional vector space, which can be used for subsequent algorithms. Negative sampling, which samples negative triplets from non-observed ones in the training data, is an important step in KG embedding. Recently, generative adversarial network (GAN), has been introduced in negative sampling. By sampling negative triplets with large scores, these methods avoid the problem of vanishing gradient and thus obtain better performance. However, using GAN makes the original model more complex and hard to train, where reinforcement learning must be used. In this paper, motivated by the observation that negative triplets with large scores are important but rare, we propose to directly keep track of them with the cache. However, how to sample from and update the cache are two important questions. We carefully design the solutions, which are not only efficient but also achieve a good balance between exploration and exploitation. In this way, our method acts as a "distilled" version of previous GA-based methods, which does not waste training time on additional parameters to fit the full distribution of negative triplets. The extensive experiments show that our method can gain significant improvement in various KG embedding models, and outperform the state-of-the-art negative sampling methods based on GAN.

Knowledge graph embedding aims to embed entities and relations of knowledge graphs into low-dimensional vector spaces. Translating embedding methods regard relations as the translation from head entities to tail entities, which achieve the state-of-the-art results among knowledge graph embedding methods. However, a major limitation of these methods is the time consuming training process, which may take several days or even weeks for large knowledge graphs, and result in great difficulty in practical applications. In this paper, we propose an efficient parallel framework for translating embedding methods, called ParTrans-X, which enables the methods to be paralleled without locks by utilizing the distinguished structures of knowledge graphs. Experiments on two datasets with three typical translating embedding methods, i.e., TransE [3], TransH [17], and a more efficient variant TransE- AdaGrad [10] validate that ParTrans-X can speed up the training process by more than an order of magnitude.