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no code implementations • ICLR 2019 • Jinghui Chen, Quanquan Gu

Experiments on standard benchmarks show that Padam can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks.

no code implementations • 13 May 2022 • Jiafan He, Dongruo Zhou, Tong Zhang, Quanquan Gu

We show that for both known $C$ and unknown $C$ cases, our algorithm with proper choice of hyperparameter achieves a regret that nearly matches the lower bounds.

no code implementations • ICLR 2022 • Yihan Wang, Zhouxing Shi, Quanquan Gu, Cho-Jui Hsieh

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training neural networks with certifiable robustness guarantees when potential adversarial perturbations present, while the convergence of IBP training remains unknown in existing literature.

no code implementations • 7 Mar 2022 • Difan Zou, Jingfeng Wu, Vladimir Braverman, Quanquan Gu, Sham M. Kakade

Stochastic gradient descent (SGD) has achieved great success due to its superior performance in both optimization and generalization.

no code implementations • 28 Feb 2022 • Heyang Zhao, Dongruo Zhou, Jiafan He, Quanquan Gu

For generalized linear bandits, we further propose an algorithm based on follow-the-regularized-leader (FTRL) subroutine and online-to-confidence-set conversion, which can achieve a tighter variance-dependent regret under certain conditions.

no code implementations • 14 Feb 2022 • Yuan Cao, Zixiang Chen, Mikhail Belkin, Quanquan Gu

In this paper, we study the benign overfitting phenomenon in training a two-layer convolutional neural network (CNN).

no code implementations • ICLR 2022 • Yiling Jia, Weitong Zhang, Dongruo Zhou, Quanquan Gu, Hongning Wang

Thanks to the power of representation learning, neural contextual bandit algorithms demonstrate remarkable performance improvement against their classical counterparts.

no code implementations • 31 Dec 2021 • Jinghui Chen, Yuan Cao, Quanquan Gu

Our result suggests that under moderate perturbations, adversarially trained linear classifiers can achieve the near-optimal standard and adversarial risks, despite overfitting the noisy training data.

no code implementations • 15 Dec 2021 • Yisen Wang, Xingjun Ma, James Bailey, JinFeng Yi, BoWen Zhou, Quanquan Gu

In this paper, we propose such a criterion, namely First-Order Stationary Condition for constrained optimization (FOSC), to quantitatively evaluate the convergence quality of adversarial examples found in the inner maximization.

no code implementations • 25 Oct 2021 • Yifei Min, Jiafan He, Tianhao Wang, Quanquan Gu

To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP.

no code implementations • NeurIPS 2021 • Zixiang Chen, Dongruo Zhou, Quanquan Gu

In this paper, we propose LENA (Last stEp shriNkAge), a faster perturbed stochastic gradient framework for finding local minima.

no code implementations • NeurIPS 2021 • Heyang Zhao, Dongruo Zhou, Quanquan Gu

We study the linear contextual bandit problem in the presence of adversarial corruption, where the interaction between the player and a possibly infinite decision set is contaminated by an adversary that can corrupt the reward up to a corruption level $C$ measured by the sum of the largest alteration on rewards in each round.

no code implementations • 19 Oct 2021 • Chonghua Liao, Jiafan He, Quanquan Gu

To the best of our knowledge, this is the first provable privacy-preserving RL algorithm with linear function approximation.

no code implementations • 14 Oct 2021 • Xiaoxia Wu, Lingxiao Wang, Irina Cristali, Quanquan Gu, Rebecca Willett

We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization.

no code implementations • 12 Oct 2021 • Jingfeng Wu, Difan Zou, Vladimir Braverman, Quanquan Gu, Sham M. Kakade

In this paper, we provide problem-dependent analysis on the last iterate risk bounds of SGD with decaying stepsize, for (overparameterized) linear regression problems.

no code implementations • NeurIPS 2021 • Weitong Zhang, Dongruo Zhou, Quanquan Gu

By constructing a special class of linear Mixture MDPs, we also prove that for any reward-free algorithm, it needs to sample at least $\tilde \Omega(H^2d\epsilon^{-2})$ episodes to obtain an $\epsilon$-optimal policy.

no code implementations • 8 Oct 2021 • Yue Wu, Tao Jin, Hao Lou, Pan Xu, Farzad Farnoud, Quanquan Gu

In heterogeneous rank aggregation problems, users often exhibit various accuracy levels when comparing pairs of items.

1 code implementation • NeurIPS 2021 • Hanxun Huang, Yisen Wang, Sarah Monazam Erfani, Quanquan Gu, James Bailey, Xingjun Ma

Specifically, we make the following key observations: 1) more parameters (higher model capacity) does not necessarily help adversarial robustness; 2) reducing capacity at the last stage (the last group of blocks) of the network can actually improve adversarial robustness; and 3) under the same parameter budget, there exists an optimal architectural configuration for adversarial robustness.

no code implementations • NeurIPS 2021 • Luyao Yuan, Dongruo Zhou, Junhong Shen, Jingdong Gao, Jeffrey L. Chen, Quanquan Gu, Ying Nian Wu, Song-Chun Zhu

Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works.

no code implementations • 25 Aug 2021 • Difan Zou, Yuan Cao, Yuanzhi Li, Quanquan Gu

In this paper, we provide a theoretical explanation for this phenomenon: we show that in the nonconvex setting of learning over-parameterized two-layer convolutional neural networks starting from the same random initialization, for a class of data distributions (inspired from image data), Adam and gradient descent (GD) can converge to different global solutions of the training objective with provably different generalization errors, even with weight decay regularization.

no code implementations • NeurIPS 2021 • Difan Zou, Jingfeng Wu, Vladimir Braverman, Quanquan Gu, Dean P. Foster, Sham M. Kakade

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches.

no code implementations • 25 Jun 2021 • Spencer Frei, Difan Zou, Zixiang Chen, Quanquan Gu

We show that there exists a universal constant $C_{\mathrm{err}}>0$ such that if a pseudolabeler $\boldsymbol{\beta}_{\mathrm{pl}}$ can achieve classification error at most $C_{\mathrm{err}}$, then for any $\varepsilon>0$, an iterative self-training algorithm initialized at $\boldsymbol{\beta}_0 := \boldsymbol{\beta}_{\mathrm{pl}}$ using pseudolabels $\hat y = \mathrm{sgn}(\langle \boldsymbol{\beta}_t, \mathbf{x}\rangle)$ and using at most $\tilde O(d/\varepsilon^2)$ unlabeled examples suffices to learn the Bayes-optimal classifier up to $\varepsilon$ error, where $d$ is the ambient dimension.

no code implementations • NeurIPS 2021 • Spencer Frei, Quanquan Gu

We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities.

no code implementations • 22 Jun 2021 • Weitong Zhang, Jiafan He, Dongruo Zhou, Amy Zhang, Quanquan Gu

The success of deep reinforcement learning (DRL) is due to the power of learning a representation that is suitable for the underlying exploration and exploitation task.

no code implementations • NeurIPS 2021 • Yifei Min, Tianhao Wang, Dongruo Zhou, Quanquan Gu

We study the off-policy evaluation (OPE) problem in reinforcement learning with linear function approximation, which aims to estimate the value function of a target policy based on the offline data collected by a behavior policy.

no code implementations • NeurIPS 2021 • Yinglun Zhu, Dongruo Zhou, Ruoxi Jiang, Quanquan Gu, Rebecca Willett, Robert Nowak

To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each arm into a lower-dimensional space and carefully deal with the induced model misspecification.

no code implementations • NeurIPS 2021 • Jiafan He, Dongruo Zhou, Quanquan Gu

The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can directly imply both PAC and high probability regret bounds, making our algorithm superior to all existing algorithms with linear function approximation.

no code implementations • NAACL 2021 • Lingxiao Wang, Kevin Huang, Tengyu Ma, Quanquan Gu, Jing Huang

The core of our algorithm is to introduce a novel variance reduction term to the gradient estimation when performing the task adaptation.

no code implementations • NeurIPS 2021 • Yuan Cao, Quanquan Gu, Mikhail Belkin

In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifier for linear classification problems.

no code implementations • 19 Apr 2021 • Difan Zou, Spencer Frei, Quanquan Gu

To the best of our knowledge, this is the first work to show that adversarial training provably yields robust classifiers in the presence of noise.

no code implementations • 23 Mar 2021 • Difan Zou, Jingfeng Wu, Vladimir Braverman, Quanquan Gu, Sham M. Kakade

More specifically, for SGD with iterate averaging, we demonstrate the sharpness of the established excess risk bound by proving a matching lower bound (up to constant factors).

no code implementations • 25 Feb 2021 • Quanquan Gu, Amin Karbasi, Khashayar Khosravi, Vahab Mirrokni, Dongruo Zhou

In many sequential decision-making problems, the individuals are split into several batches and the decision-maker is only allowed to change her policy at the end of batches.

no code implementations • 17 Feb 2021 • Jiafan He, Dongruo Zhou, Quanquan Gu

In this paper, we study RL in episodic MDPs with adversarial reward and full information feedback, where the unknown transition probability function is a linear function of a given feature mapping, and the reward function can change arbitrarily episode by episode.

no code implementations • 15 Feb 2021 • Zixiang Chen, Dongruo Zhou, Quanquan Gu

To assess the optimality of our algorithm, we also prove an $\tilde{\Omega}( dH\sqrt{T})$ lower bound on the regret.

no code implementations • 15 Feb 2021 • Yue Wu, Dongruo Zhou, Quanquan Gu

We study reinforcement learning in an infinite-horizon average-reward setting with linear function approximation, where the transition probability function of the underlying Markov Decision Process (MDP) admits a linear form over a feature mapping of the current state, action, and next state.

no code implementations • NeurIPS 2021 • Tianhao Wang, Dongruo Zhou, Quanquan Gu

In specific, for the batch learning model, our proposed LSVI-UCB-Batch algorithm achieves an $\tilde O(\sqrt{d^3H^3T} + dHT/B)$ regret, where $d$ is the dimension of the feature mapping, $H$ is the episode length, $T$ is the number of interactions and $B$ is the number of batches.

1 code implementation • 4 Jan 2021 • Spencer Frei, Yuan Cao, Quanquan Gu

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization.

no code implementations • 15 Dec 2020 • Dongruo Zhou, Quanquan Gu, Csaba Szepesvari

Based on the new inequality, we propose a new, computationally efficient algorithm with linear function approximation named $\text{UCRL-VTR}^{+}$ for the aforementioned linear mixture MDPs in the episodic undiscounted setting.

no code implementations • NeurIPS 2021 • Pan Xu, Zheng Wen, Handong Zhao, Quanquan Gu

We study a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the reward generating function is unknown.

no code implementations • NeurIPS 2020 • Yue Wu, Weitong Zhang, Pan Xu, Quanquan Gu

In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i. i. d.

no code implementations • 23 Nov 2020 • Jiafan He, Dongruo Zhou, Quanquan Gu

Reinforcement learning (RL) with linear function approximation has received increasing attention recently.

no code implementations • 19 Nov 2020 • Dongruo Zhou, Jiahao Chen, Quanquan Gu

Multi-objective reinforcement learning (MORL) is an extension of ordinary, single-objective reinforcement learning (RL) that is applicable to many real-world tasks where multiple objectives exist without known relative costs.

no code implementations • ICLR 2021 • Jingfeng Wu, Difan Zou, Vladimir Braverman, Quanquan Gu

Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory.

no code implementations • 19 Oct 2020 • Difan Zou, Pan Xu, Quanquan Gu

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave.

1 code implementation • 3 Oct 2020 • Jinghui Chen, Yu Cheng, Zhe Gan, Quanquan Gu, Jingjing Liu

In this work, we develop a new understanding towards Fast Adversarial Training, by viewing random initialization as performing randomized smoothing for better optimization of the inner maximization problem.

1 code implementation • NeurIPS 2021 • Boxi Wu, Jinghui Chen, Deng Cai, Xiaofei He, Quanquan Gu

Previous empirical results suggest that adversarial training requires wider networks for better performances.

3 code implementations • ICLR 2021 • Weitong Zhang, Dongruo Zhou, Lihong Li, Quanquan Gu

Thompson Sampling (TS) is one of the most effective algorithms for solving contextual multi-armed bandit problems.

no code implementations • NeurIPS 2021 • Jiafan He, Dongruo Zhou, Quanquan Gu

We study the reinforcement learning problem for discounted Markov Decision Processes (MDPs) under the tabular setting.

no code implementations • 1 Oct 2020 • Spencer Frei, Yuan Cao, Quanquan Gu

We analyze the properties of gradient descent on convex surrogates for the zero-one loss for the agnostic learning of linear halfspaces.

no code implementations • 23 Jun 2020 • Dongruo Zhou, Jiafan He, Quanquan Gu

We propose a novel algorithm that makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-\gamma)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $\gamma$ is the discount factor of the MDP.

1 code implementation • 23 Jun 2020 • Jinghui Chen, Quanquan Gu

Deep neural networks are vulnerable to adversarial attacks.

Ranked #1 on Hard-label Attack on CIFAR-10

no code implementations • ICML 2020 • Yonatan Dukler, Quanquan Gu, Guido Montúfar

The success of deep neural networks is in part due to the use of normalization layers.

no code implementations • NeurIPS 2020 • Spencer Frei, Yuan Cao, Quanquan Gu

In the agnostic PAC learning setting, where no assumption on the relationship between the labels $y$ and the input $x$ is made, if the optimal population risk is $\mathsf{OPT}$, we show that gradient descent achieves population risk $O(\mathsf{OPT})+\epsilon$ in polynomial time and sample complexity when $\sigma$ is strictly increasing.

1 code implementation • 21 May 2020 • Bargav Jayaraman, Lingxiao Wang, Katherine Knipmeyer, Quanquan Gu, David Evans

Since previous inference attacks fail in imbalanced prior setting, we develop a new inference attack based on the intuition that inputs corresponding to training set members will be near a local minimum in the loss function, and show that an attack that combines this with thresholds on the per-instance loss can achieve high PPV even in settings where other attacks appear to be ineffective.

no code implementations • 4 May 2020 • Yue Wu, Weitong Zhang, Pan Xu, Quanquan Gu

In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i. i. d.

no code implementations • ICLR 2020 • Lingxiao Wang, Jing Huang, Kevin Huang, Ziniu Hu, Guangtao Wang, Quanquan Gu

Recent Transformer-based models such as Transformer-XL and BERT have achieved huge success on various natural language processing tasks.

no code implementations • 1 May 2020 • Zhicong Liang, Bao Wang, Quanquan Gu, Stanley Osher, Yuan YAO

Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users.

no code implementations • ICLR 2020 • Yisen Wang, Difan Zou, Jin-Feng Yi, James Bailey, Xingjun Ma, Quanquan Gu

In this paper, we investigate the distinctive influence of misclassified and correctly classified examples on the final robustness of adversarial training.

no code implementations • 3 Mar 2020 • Tianyuan Jin, Pan Xu, Jieming Shi, Xiaokui Xiao, Quanquan Gu

Thompson sampling is one of the most widely used algorithms for many online decision problems, due to its simplicity in implementation and superior empirical performance over other state-of-the-art methods.

no code implementations • ICLR 2020 • Difan Zou, Philip M. Long, Quanquan Gu

We further propose a modified identity input and output transformations, and show that a $(d+k)$-wide neural network is sufficient to guarantee the global convergence of GD/SGD, where $d, k$ are the input and output dimensions respectively.

1 code implementation • 1 Mar 2020 • Xiao Zhang, Jinghui Chen, Quanquan Gu, David Evans

Starting with Gilmer et al. (2018), several works have demonstrated the inevitability of adversarial examples based on different assumptions about the underlying input probability space.

no code implementations • 21 Feb 2020 • Tianyuan Jin, Pan Xu, Xiaokui Xiao, Quanquan Gu

In this paper, we show that a variant of ETC algorithm can actually achieve the asymptotic optimality for multi-armed bandit problems as UCB-type algorithms do and extend it to the batched bandit setting.

no code implementations • NeurIPS 2020 • Zixiang Chen, Yuan Cao, Quanquan Gu, Tong Zhang

In this paper, we provide a generalized neural tangent kernel analysis and show that noisy gradient descent with weight decay can still exhibit a "kernel-like" behavior.

no code implementations • 10 Dec 2019 • Pan Xu, Quanquan Gu

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms.

no code implementations • 3 Dec 2019 • Yuan Cao, Zhiying Fang, Yue Wu, Ding-Xuan Zhou, Quanquan Gu

An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions.

no code implementations • 3 Dec 2019 • Tao Jin, Pan Xu, Quanquan Gu, Farzad Farnoud

By allowing different noise distributions, the proposed HTM model maintains the generality of Thurstone's original framework, and as such, also extends the Bradley-Terry-Luce (BTL) model for pairwise comparisons to heterogeneous populations of users.

1 code implementation • NeurIPS 2019 • Difan Zou, Pan Xu, Quanquan Gu

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) algorithms have received increasing attention in both theory and practice.

no code implementations • ICLR 2021 • Zixiang Chen, Yuan Cao, Difan Zou, Quanquan Gu

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $\epsilon^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy nice optimization and generalization guarantees.

1 code implementation • NeurIPS 2019 • Difan Zou, Ziniu Hu, Yewen Wang, Song Jiang, Yizhou Sun, Quanquan Gu

Original full-batch GCN training requires calculating the representation of all the nodes in the graph per GCN layer, which brings in high computation and memory costs.

no code implementations • NeurIPS 2019 • Yuan Cao, Quanquan Gu

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters.

2 code implementations • ICML 2020 • Dongruo Zhou, Lihong Li, Quanquan Gu

To the best of our knowledge, it is the first neural network-based contextual bandit algorithm with a near-optimal regret guarantee.

1 code implementation • 2 Nov 2019 • Bao Wang, Difan Zou, Quanquan Gu, Stanley Osher

As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling.

no code implementations • 30 Oct 2019 • Lingxiao Wang, Bargav Jayaraman, David Evans, Quanquan Gu

While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge.

no code implementations • NeurIPS 2019 • Spencer Frei, Yuan Cao, Quanquan Gu

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased training stability and generalization performance with this architecture, although there has been limited theoretical understanding for this improvement.

no code implementations • 25 Sep 2019 • Jinghui Chen, Dongruo Zhou, Yiqi Tang, Ziyan Yang, Yuan Cao, Quanquan Gu

Experiments on standard benchmarks show that our proposed algorithm can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks.

no code implementations • 25 Sep 2019 • Yonatan Dukler, Quanquan Gu, Guido Montufar

We present a proof of convergence for ReLU networks trained with weight normalization.

no code implementations • 25 Sep 2019 • Dongruo Zhou, Lihong Li, Quanquan Gu

To the best of our knowledge, our algorithm is the first neural network-based contextual bandit algorithm with near-optimal regret guarantee.

1 code implementation • ICLR 2020 • Pan Xu, Felicia Gao, Quanquan Gu

Improving the sample efficiency in reinforcement learning has been a long-standing research problem.

no code implementations • 13 Sep 2019 • Lingxiao Wang, Quanquan Gu

We study the problem of estimating high dimensional models with underlying sparse structures while preserving the privacy of each training example.

1 code implementation • 28 Jun 2019 • Bao Wang, Quanquan Gu, March Boedihardjo, Farzin Barekat, Stanley J. Osher

At the core of DP-LSSGD is the Laplacian smoothing, which smooths out the Gaussian noise used in the Gaussian mechanism.

no code implementations • NeurIPS 2019 • Difan Zou, Quanquan Gu

A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i. e., sufficiently wide) deep neural networks.

no code implementations • NeurIPS 2019 • Yuan Cao, Quanquan Gu

We study the training and generalization of deep neural networks (DNNs) in the over-parameterized regime, where the network width (i. e., number of hidden nodes per layer) is much larger than the number of training data points.

no code implementations • 29 May 2019 • Pan Xu, Felicia Gao, Quanquan Gu

We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning.

no code implementations • 4 Feb 2019 • Yuan Cao, Quanquan Gu

However, existing generalization error bounds are unable to explain the good generalization performance of over-parameterized DNNs.

no code implementations • 31 Jan 2019 • Dongruo Zhou, Quanquan Gu

We prove tight lower bounds for the complexity of finding $\epsilon$-suboptimal point and $\epsilon$-approximate stationary point in different settings, for a wide regime of the smallest eigenvalue of the Hessian of the objective function (or each component function).

no code implementations • 31 Jan 2019 • Dongruo Zhou, Quanquan Gu

Built upon SRVRC, we further propose a Hessian-free SRVRC algorithm, namely SRVRC$_{\text{free}}$, which only requires stochastic gradient and Hessian-vector product computations, and achieves $\tilde O(dn\epsilon^{-2} \land d\epsilon^{-3})$ runtime complexity, where $n$ is the number of component functions in the finite-sum structure, $d$ is the problem dimension, and $\epsilon$ is the optimization precision.

no code implementations • NeurIPS 2018 • Dongruo Zhou, Pan Xu, Quanquan Gu

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions.

1 code implementation • NeurIPS 2018 • Bargav Jayaraman, Lingxiao Wang, David Evans, Quanquan Gu

We explore two popular methods of differential privacy, output perturbation and gradient perturbation, and advance the state-of-the-art for both methods in the distributed learning setting.

no code implementations • NeurIPS 2018 • Yaodong Yu, Pan Xu, Quanquan Gu

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.

no code implementations • 29 Nov 2018 • Dongruo Zhou, Pan Xu, Quanquan Gu

The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods.

2 code implementations • ICLR 2019 • Jinghui Chen, Dongruo Zhou, Jin-Feng Yi, Quanquan Gu

Depending on how much information an adversary can access to, adversarial attacks can be classified as white-box attack and black-box attack.

no code implementations • 21 Nov 2018 • Difan Zou, Yuan Cao, Dongruo Zhou, Quanquan Gu

In particular, we study the binary classification problem and show that for a broad family of loss functions, with proper random weight initialization, both gradient descent and stochastic gradient descent can find the global minima of the training loss for an over-parameterized deep ReLU network, under mild assumption on the training data.

no code implementations • 16 Aug 2018 • Dongruo Zhou, Jinghui Chen, Yuan Cao, Yiqi Tang, Ziyan Yang, Quanquan Gu

In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad.

no code implementations • ICML 2018 • Pan Xu, Tianhao Wang, Quanquan Gu

We provide a second-order stochastic differential equation (SDE), which characterizes the continuous-time dynamics of accelerated stochastic mirror descent (ASMD) for strongly convex functions.

no code implementations • ICML 2018 • Jinghui Chen, Pan Xu, Lingxiao Wang, Jian Ma, Quanquan Gu

We propose a nonconvex estimator for the covariate adjusted precision matrix estimation problem in the high dimensional regime, under sparsity constraints.

no code implementations • ICML 2018 • Xiao Zhang, Lingxiao Wang, Yaodong Yu, Quanquan Gu

We propose a primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery.

no code implementations • 22 Jun 2018 • Dongruo Zhou, Pan Xu, Quanquan Gu

For general stochastic optimization problems, the proposed $\text{SNVRG}^{+}+\text{Neon2}^{\text{online}}$ achieves $\tilde{O}(\epsilon^{-3}+\epsilon_H^{-5}+\epsilon^{-2}\epsilon_H^{-3})$ gradient complexity, which is better than both $\text{SVRG}+\text{Neon2}^{\text{online}}$ (Allen-Zhu and Li, 2017) and Natasha2 (Allen-Zhu, 2017) in certain regimes.

no code implementations • 20 Jun 2018 • Xiao Zhang, Yaodong Yu, Lingxiao Wang, Quanquan Gu

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network.

no code implementations • NeurIPS 2018 • Dongruo Zhou, Pan Xu, Quanquan Gu

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions.

5 code implementations • 18 Jun 2018 • Jinghui Chen, Dongruo Zhou, Yiqi Tang, Ziyan Yang, Yuan Cao, Quanquan Gu

Experiments on standard benchmarks show that our proposed algorithm can maintain a fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks.

1 code implementation • ICML 2018 • Xiao Zhang, Simon S. Du, Quanquan Gu

We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information.

no code implementations • ICML 2018 • Dongruo Zhou, Pan Xu, Quanquan Gu

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.

no code implementations • ICML 2018 • Difan Zou, Pan Xu, Quanquan Gu

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution.

no code implementations • 18 Dec 2017 • Yaodong Yu, Pan Xu, Quanquan Gu

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.

no code implementations • 11 Dec 2017 • Yaodong Yu, Difan Zou, Quanquan Gu

We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity.

no code implementations • NeurIPS 2017 • Pan Xu, Jian Ma, Quanquan Gu

In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization and an efficient alternating gradient descent algorithm with hard thresholding to solve it.

no code implementations • ICML 2017 • Rongda Zhu, Lingxiao Wang, ChengXiang Zhai, Quanquan Gu

We apply our generic algorithm to two illustrative latent variable models: Gaussian mixture model and mixture of linear regression, and demonstrate the advantages of our algorithm by both theoretical analysis and numerical experiments.

no code implementations • ICML 2017 • Lingxiao Wang, Xiao Zhang, Quanquan Gu

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery.

no code implementations • ICML 2017 • Aditya Chaudhry, Pan Xu, Quanquan Gu

Causal inference among high-dimensional time series data proves an important research problem in many fields.

no code implementations • ICML 2017 • Lingxiao Wang, Quanquan Gu

In particular, we show that provided that the number of corrupted samples $n_2$ for each variable satisfies $n_2 \lesssim \sqrt{n}/\sqrt{\log d}$, where $n$ is the sample size and $d$ is the number of variables, the proposed robust precision matrix estimator attains the same statistical rate as the standard estimator for Gaussian graphical models.

no code implementations • NeurIPS 2018 • Pan Xu, Jinghui Chen, Difan Zou, Quanquan Gu

Furthermore, for the first time we prove the global convergence guarantee for variance reduced stochastic gradient Langevin dynamics (SVRG-LD) to the almost minimizer within $\tilde O\big(\sqrt{n}d^5/(\lambda^4\epsilon^{5/2})\big)$ stochastic gradient evaluations, which outperforms the gradient complexities of GLD and SGLD in a wide regime.

no code implementations • 20 Apr 2017 • Jinghui Chen, Lingxiao Wang, Xiao Zhang, Quanquan Gu

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise.

no code implementations • NeurIPS 2017 • Pan Xu, Jian Ma, Quanquan Gu

In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization, and an efficient alternating gradient descent algorithm with hard thresholding to solve it.

no code implementations • 21 Feb 2017 • Xiao Zhang, Lingxiao Wang, Quanquan Gu

We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness conditions.

no code implementations • 9 Jan 2017 • Lingxiao Wang, Xiao Zhang, Quanquan Gu

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery.

no code implementations • 2 Jan 2017 • Xiao Zhang, Lingxiao Wang, Quanquan Gu

And in the noiseless setting, our algorithm is guaranteed to linearly converge to the unknown low-rank matrix and achieves exact recovery with optimal sample complexity.

no code implementations • 29 Dec 2016 • Pan Xu, Lu Tian, Quanquan Gu

In detail, the proposed method distributes the $d$-dimensional data of size $N$ generated from a transelliptical graphical model into $m$ worker machines, and estimates the latent precision matrix on each worker machine based on the data of size $n=N/m$.

no code implementations • NeurIPS 2016 • Pan Xu, Quanquan Gu

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network.

no code implementations • 17 Oct 2016 • Lingxiao Wang, Xiao Zhang, Quanquan Gu

In the general case with noisy observations, we show that our algorithm is guaranteed to linearly converge to the unknown low-rank matrix up to minimax optimal statistical error, provided an appropriate initial estimator.

no code implementations • 15 Oct 2016 • Lu Tian, Quanquan Gu

We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime.

no code implementations • 2 Jun 2016 • Jinghui Chen, Quanquan Gu

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints.

no code implementations • 30 Dec 2015 • Zhaoran Wang, Quanquan Gu, Han Liu

Based upon an oracle model of computation, which captures the interactions between algorithms and data, we establish a general lower bound that explicitly connects the minimum testing risk under computational budget constraints with the intrinsic probabilistic and combinatorial structures of statistical problems.

no code implementations • NeurIPS 2015 • Zhaoran Wang, Quanquan Gu, Yang Ning, Han Liu

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models.

no code implementations • 18 May 2015 • Huan Gui, Quanquan Gu

Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i. e., exactly recovers the true rank of the matrix), besides attaining a faster rate.

no code implementations • 4 Mar 2015 • Zhaoran Wang, Quanquan Gu, Han Liu

Many high dimensional sparse learning problems are formulated as nonconvex optimization.

no code implementations • 9 Feb 2015 • Quanquan Gu, Yuan Cao, Yang Ning, Han Liu

Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach.

no code implementations • 30 Dec 2014 • Zhaoran Wang, Quanquan Gu, Yang Ning, Han Liu

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models.

no code implementations • NeurIPS 2014 • Quanquan Gu, Zhaoran Wang, Han Liu

In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-$k$, and attains a $\sqrt{s/n}$ statistical rate of convergence with $s$ being the subspace sparsity level and $n$ the sample size.

no code implementations • NeurIPS 2014 • Quanquan Gu, Huan Gui, Jiawei Han

In this paper, we study the statistical performance of robust tensor decomposition with gross corruption.

no code implementations • NeurIPS 2012 • Quanquan Gu, Tong Zhang, Jiawei Han, Chris H. Ding

In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound.

1 code implementation • 14 Feb 2012 • Quanquan Gu, Zhenhui Li, Jiawei Han

Fisher score is one of the most widely used supervised feature selection methods.

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