OpenRaiser/Intern-Atlas huggingface dataset:
Improving the Privacy and Accuracy of ADMM-Based Distributed Algorithms
Venue: Conference ICML 2018
Year: 2018

Alternating direction method of multiplier (ADMM) is a popular method used to design distributed versions of a machine learning algorithm, whereby local computations are performed on local data with the output exchanged among neighbors in an iterative fashion. During this iterative process the leakage of data privacy arises. A differentially private ADMM was proposed in prior work (Zhang & Zhu, 2017) where only the privacy loss of a single node during one iteration was bounded, a method that makes it difficult to balance the tradeoff between the utility attained through distributed computation and privacy guarantees when considering the total privacy loss of all nodes over the entire iterative process. We propose a perturbation method for ADMM where the perturbed term is correlated with the penalty parameters; this is shown to improve the utility and privacy simultaneously. The method is based on a modified ADMM where each node independently determines its own penalty parameter in every iteration and decouples it from the dual updating step size. The condition for convergence of the modified ADMM and the lower bound on the convergence rate are also derived.
Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization
Venue: Conference ICML 2018
Year: 2018

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that arise in its training. Specifically, we parameterize the transition matrix by its singular value decomposition(SVD), which allows us to explicitly track and control its singular values. We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. By explicitly controlling the singular values, our proposed Spectral-RNN method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent. We note that the SVD parameterization can be used for any rectangular weight matrix, hence it can be easily extended to any deep neural network, such as a multi-layer perceptron. Theoretically, we demonstrate that our parameterization does not lose any expressive power, and show how it controls generalization of RNN for the classification task. %, and show how it potentially makes the optimization process easier. Our extensive experimental results also demonstrate that the proposed framework converges faster, and has good generalization, especially in capturing long range dependencies, as shown on the synthetic addition and copy tasks, as well as on MNIST and Penn Tree Bank data sets.
Learning Long Term Dependencies via Fourier Recurrent Units
Venue: Conference ICML 2018
Year: 2018

It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, the Fourier Recurrent Unit (FRU), that stabilizes the gradients that arise in its training while giving us stronger expressive power. Specifically, FRU summarizes the hidden states $h^{(t)}$ along the temporal dimension with Fourier basis functions. This allows gradients to easily reach any layer due to FRU's residual learning structure and the global support of trigonometric functions. We show that FRU has gradient lower and upper bounds independent of temporal dimension. We also show the strong expressivity of sparse Fourier basis, from which FRU obtains its strong expressive power. Our experimental study also demonstrates that with fewer parameters the proposed architecture outperforms other recurrent architectures on many tasks.
Tropical Geometry of Deep Neural Networks
Venue: Conference ICML 2018
Year: 2018

We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden layer can be characterized by zonotopes, which serve as building blocks for deeper networks; we relate decision boundaries of such neural networks to tropical hypersurfaces, a major object of study in tropical geometry; and we prove that linear regions of such neural networks correspond to vertices of polytopes associated with tropical rational functions. An insight from our tropical formulation is that a deeper network is exponentially more expressive than a shallow network.
Noisy Natural Gradient as Variational Inference
Venue: Conference ICML 2018
Year: 2018

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo's predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.
Dynamic Regret of Strongly Adaptive Methods
Venue: Conference ICML 2018
Year: 2018

To cope with changing environments, recent developments in online learning have introduced the concepts of adaptive regret and dynamic regret independently. In this paper, we illustrate an intrinsic connection between these two concepts by showing that the dynamic regret can be expressed in terms of the adaptive regret and the functional variation. This observation implies that strongly adaptive algorithms can be directly leveraged to minimize the dynamic regret. As a result, we present a series of strongly adaptive algorithms that have small dynamic regrets for convex functions, exponentially concave functions, and strongly convex functions, respectively. To the best of our knowledge, this is the first time that exponential concavity is utilized to upper bound the dynamic regret. Moreover, all of those adaptive algorithms do not need any prior knowledge of the functional variation, which is a significant advantage over previous specialized methods for minimizing dynamic regret.
Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents
Venue: Conference ICML 2018
Year: 2018

We consider the problem of \emph{fully decentralized} multi-agent reinforcement learning (MARL), where the agents are located at the nodes of a time-varying communication network. Specifically, we assume that the reward functions of the agents might correspond to different tasks, and are only known to the corresponding agent. Moreover, each agent makes individual decisions based on both the information observed locally and the messages received from its neighbors over the network. Within this setting, the collective goal of the agents is to maximize the globally averaged return over the network through exchanging information with their neighbors. To this end, we propose two decentralized actor-critic algorithms with function approximation, which are applicable to large-scale MARL problems where both the number of states and the number of agents are massively large. Under the decentralized structure, the actor step is performed individually by each agent with no need to infer the policies of others. For the critic step, we propose a consensus update via communication over the network. Our algorithms are fully incremental and can be implemented in an online fashion. Convergence analyses of the algorithms are provided when the value functions are approximated within the class of linear functions. Extensive simulation results with both linear and nonlinear function approximations are presented to validate the proposed algorithms. Our work appears to be the first study of fully decentralized MARL algorithms for networked agents with function approximation, with provable convergence guarantees.
MSplit LBI: Realizing Feature Selection and Dense Estimation Simultaneously in Few-shot and Zero-shot Learning
Venue: Conference ICML 2018
Year: 2018

It is one typical and general topic of learning a good embedding model to efficiently learn the representation coefficients between two spaces/subspaces. To solve this task, $L_{1}$ regularization is widely used for the pursuit of feature selection and avoiding overfitting, and yet the sparse estimation of features in $L_{1}$ regularization may cause the underfitting of training data. $L_{2}$ regularization is also frequently used, but it is a biased estimator. In this paper, we propose the idea that the features consist of three orthogonal parts, \emph{namely} sparse strong signals, dense weak signals and random noise, in which both strong and weak signals contribute to the fitting of data. To facilitate such novel decomposition, \emph{MSplit} LBI is for the first time proposed to realize feature selection and dense estimation simultaneously. We provide theoretical and simulational verification that our method exceeds $L_{1}$ and $L_{2}$ regularization, and extensive experimental results show that our method achieves state-of-the-art performance in the few-shot and zero-shot learning.
Composite Marginal Likelihood Methods for Random Utility Models
Venue: Conference ICML 2018
Year: 2018

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computational efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.
Understanding Generalization and Optimization Performance of Deep CNNs
Venue: Conference ICML 2018
Year: 2018

This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based training algorithms. Specifically, for a CNN model consisting of $l$ convolutional layers and one fully connected layer, we prove that its generalization error is bounded by $\mathcal{O}(\sqrt{\dt\widetilde{\varrho}/n})$ where $θ$ denotes freedom degree of the network parameters and $\widetilde{\varrho}=\mathcal{O}(\log(\prod_{i=1}^{l}\rwi{i} (\ki{i}-\si{i}+1)/p)+\log(\rf))$ encapsulates architecture parameters including the kernel size $\ki{i}$, stride $\si{i}$, pooling size $p$ and parameter magnitude $\rwi{i}$. To our best knowledge, this is the first generalization bound that only depends on $\mathcal{O}(\log(\prod_{i=1}^{l+1}\rwi{i}))$, tighter than existing ones that all involve an exponential term like $\mathcal{O}(\prod_{i=1}^{l+1}\rwi{i})$. Besides, we prove that for an arbitrary gradient descent algorithm, the computed approximate stationary point by minimizing empirical risk is also an approximate stationary point to the population risk. This well explains why gradient descent training algorithms usually perform sufficiently well in practice. Furthermore, we prove the one-to-one correspondence and convergence guarantees for the non-degenerate stationary points between the empirical and population risks. It implies that the computed local minimum for the empirical risk is also close to a local minimum for the population risk, thus ensuring the good generalization performance of CNNs.
A Simple Stochastic Variance Reduced Algorithm with Fast Convergence Rates
Venue: Conference ICML 2018
Year: 2018

Recent years have witnessed exciting progress in the study of stochastic variance reduced gradient methods (e.g., SVRG, SAGA), their accelerated variants (e.g, Katyusha) and their extensions in many different settings (e.g., online, sparse, asynchronous, distributed). Among them, accelerated methods enjoy improved convergence rates but have complex coupling structures, which makes them hard to be extended to more settings (e.g., sparse and asynchronous) due to the existence of perturbation. In this paper, we introduce a simple stochastic variance reduced algorithm (MiG), which enjoys the best-known convergence rates for both strongly convex and non-strongly convex problems. Moreover, we also present its efficient sparse and asynchronous variants, and theoretically analyze its convergence rates in these settings. Finally, extensive experiments for various machine learning problems such as logistic regression are given to illustrate the practical improvement in both serial and asynchronous settings.
Stochastic Variance-Reduced Cubic Regularized Newton Method
Venue: Conference ICML 2018
Year: 2018

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. We show that our algorithm is guaranteed to converge to an $(ε,\sqrtε)$-approximately local minimum within $\tilde{O}(n^{4/5}/ε^{3/2})$ second-order oracle calls, which outperforms the state-of-the-art cubic regularization algorithms including subsampled cubic regularization. Our work also sheds light on the application of variance reduction technique to high-order non-convex optimization methods. Thorough experiments on various non-convex optimization problems support our theory.
Submodular Streaming in All Its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity
Venue: Conference ICML 2019
Year: 2019

Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a cardinality constraint $k$. We first propose Sieve-Streaming++, which requires just one pass over the data, keeps only $O(k)$ elements and achieves the tight $(1/2)$-approximation guarantee. The best previously known streaming algorithms either achieve a suboptimal $(1/4)$-approximation with $Θ(k)$ memory or the optimal $(1/2)$-approximation with $O(k\log k)$ memory. Next, we show that by buffering a small fraction of the stream and applying a careful filtering procedure, one can heavily reduce the number of adaptive computational rounds, thus substantially lowering the computational complexity of Sieve-Streaming++. We then generalize our results to the more challenging multi-source streaming setting. We show how one can achieve the tight $(1/2)$-approximation guarantee with $O(k)$ shared memory while minimizing not only the required rounds of computations but also the total number of communicated bits. Finally, we demonstrate the efficiency of our algorithms on real-world data summarization tasks for multi-source streams of tweets and of YouTube videos.
Target-Based Temporal-Difference Learning
Venue: Conference ICML 2019
Year: 2019

The use of target networks has been a popular and key component of recent deep Q-learning algorithms for reinforcement learning, yet little is known from the theory side. In this work, we introduce a new family of target-based temporal difference (TD) learning algorithms and provide theoretical analysis on their convergences. In contrast to the standard TD-learning, target-based TD algorithms maintain two separate learning parameters-the target variable and online variable. Particularly, we introduce three members in the family, called the averaging TD, double TD, and periodic TD, where the target variable is updated through an averaging, symmetric, or periodic fashion, mirroring those techniques used in deep Q-learning practice. We establish asymptotic convergence analyses for both averaging TD and double TD and a finite sample analysis for periodic TD. In addition, we also provide some simulation results showing potentially superior convergence of these target-based TD algorithms compared to the standard TD-learning. While this work focuses on linear function approximation and policy evaluation setting, we consider this as a meaningful step towards the theoretical understanding of deep Q-learning variants with target networks.
Exploring interpretable LSTM neural networks over multi-variable data
Venue: Conference ICML 2019
Year: 2019

For recurrent neural networks trained on time series with target and exogenous variables, in addition to accurate prediction, it is also desired to provide interpretable insights into the data. In this paper, we explore the structure of LSTM recurrent neural networks to learn variable-wise hidden states, with the aim to capture different dynamics in multi-variable time series and distinguish the contribution of variables to the prediction. With these variable-wise hidden states, a mixture attention mechanism is proposed to model the generative process of the target. Then we develop associated training methods to jointly learn network parameters, variable and temporal importance w.r.t the prediction of the target variable. Extensive experiments on real datasets demonstrate enhanced prediction performance by capturing the dynamics of different variables. Meanwhile, we evaluate the interpretation results both qualitatively and quantitatively. It exhibits the prospect as an end-to-end framework for both forecasting and knowledge extraction over multi-variable data.
Bridging Theory and Algorithm for Domain Adaptation
Venue: Conference ICML 2019
Year: 2019

This paper addresses the problem of unsupervised domain adaption from theoretical and algorithmic perspectives. Existing domain adaptation theories naturally imply minimax optimization algorithms, which connect well with the domain adaptation methods based on adversarial learning. However, several disconnections still exist and form the gap between theory and algorithm. We extend previous theories (Mansour et al., 2009c; Ben-David et al., 2010) to multiclass classification in domain adaptation, where classifiers based on the scoring functions and margin loss are standard choices in algorithm design. We introduce Margin Disparity Discrepancy, a novel measurement with rigorous generalization bounds, tailored to the distribution comparison with the asymmetric margin loss, and to the minimax optimization for easier training. Our theory can be seamlessly transformed into an adversarial learning algorithm for domain adaptation, successfully bridging the gap between theory and algorithm. A series of empirical studies show that our algorithm achieves the state of the art accuracies on challenging domain adaptation tasks.
Provably Efficient Imitation Learning from Observation Alone
Venue: Conference ICML 2019
Year: 2019

We study Imitation Learning (IL) from Observations alone (ILFO) in large-scale MDPs. While most IL algorithms rely on an expert to directly provide actions to the learner, in this setting the expert only supplies sequences of observations. We design a new model-free algorithm for ILFO, Forward Adversarial Imitation Learning (FAIL), which learns a sequence of time-dependent policies by minimizing an Integral Probability Metric between the observation distributions of the expert policy and the learner. FAIL is the first provably efficient algorithm in ILFO setting, which learns a near-optimal policy with a number of samples that is polynomial in all relevant parameters but independent of the number of unique observations. The resulting theory extends the domain of provably sample efficient learning algorithms beyond existing results, which typically only consider tabular reinforcement learning settings or settings that require access to a near-optimal reset distribution. We also investigate the extension of FAIL in a model-based setting. Finally we demonstrate the efficacy of FAIL on multiple OpenAI Gym control tasks.
Batch Policy Learning under Constraints
Venue: Conference ICML 2019
Year: 2019

When learning policies for real-world domains, two important questions arise: (i) how to efficiently use pre-collected off-policy, non-optimal behavior data; and (ii) how to mediate among different competing objectives and constraints. We thus study the problem of batch policy learning under multiple constraints, and offer a systematic solution. We first propose a flexible meta-algorithm that admits any batch reinforcement learning and online learning procedure as subroutines. We then present a specific algorithmic instantiation and provide performance guarantees for the main objective and all constraints. To certify constraint satisfaction, we propose a new and simple method for off-policy policy evaluation (OPE) and derive PAC-style bounds. Our algorithm achieves strong empirical results in different domains, including in a challenging problem of simulated car driving subject to multiple constraints such as lane keeping and smooth driving. We also show experimentally that our OPE method outperforms other popular OPE techniques on a standalone basis, especially in a high-dimensional setting.
Tight Kernel Query Complexity of Kernel Ridge Regression and Kernel $k$-means Clustering
Venue: Conference ICML 2019
Year: 2019

We present tight lower bounds on the number of kernel evaluations required to approximately solve kernel ridge regression (KRR) and kernel $k$-means clustering (KKMC) on $n$ input points. For KRR, our bound for relative error approximation to the minimizer of the objective function is $Ω(nd_{\mathrm{eff}}^λ/\varepsilon)$ where $d_{\mathrm{eff}}^λ$ is the effective statistical dimension, which is tight up to a $\log(d_{\mathrm{eff}}^λ/\varepsilon)$ factor. For KKMC, our bound for finding a $k$-clustering achieving a relative error approximation of the objective function is $Ω(nk/\varepsilon)$, which is tight up to a $\log(k/\varepsilon)$ factor. Our KRR result resolves a variant of an open question of El Alaoui and Mahoney, asking whether the effective statistical dimension is a lower bound on the sampling complexity or not. Furthermore, for the important practical case when the input is a mixture of Gaussians, we provide a KKMC algorithm which bypasses the above lower bound.
Hyperbolic Disk Embeddings for Directed Acyclic Graphs
Venue: Conference ICML 2019
Year: 2019

Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of nodes are exponentially increasing is difficult. Tackling in this problem, we develop Disk Embeddings, which is a framework for embedding DAGs into quasi-metric spaces. Existing state-of-the-art methods, Order Embeddings and Hyperbolic Entailment Cones, are instances of Disk Embedding in Euclidean space and spheres respectively. Furthermore, we propose a novel method Hyperbolic Disk Embeddings to handle exponential growth of relations. The results of our experiments show that our Disk Embedding models outperform existing methods especially in complex DAGs other than trees.