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Found 181 papers, 33 papers with code
Generalized Fisher Score for Feature Selection
Fisher score is one of the most widely used supervised feature selection methods.
Selective Labeling via Error Bound Minimization
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.
Robust Tensor Decomposition with Gross Corruption
In this paper, we study the statistical performance of robust tensor decomposition with gross corruption.
High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models.
Local and Global Inference for High Dimensional Nonparanormal Graphical Models
Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach.
Statistical Limits of Convex Relaxations
Many high dimensional sparse learning problems are formulated as nonconvex optimization.
Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation
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.
High Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models.
Sharp Computational-Statistical Phase Transitions via Oracle Computational Model
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.
High Dimensional Multivariate Regression and Precision Matrix Estimation via Nonconvex Optimization
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints.
Communication-efficient Distributed Sparse Linear Discriminant Analysis
We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime.
A Unified Computational and Statistical Framework for Nonconvex Low-Rank Matrix Estimation
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.
Semiparametric Differential Graph Models
In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network.
Communication-efficient Distributed Estimation and Inference for Transelliptical Graphical Models
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 $n=N/m$.
Stochastic Variance-reduced Gradient Descent for Low-rank Matrix Recovery from Linear Measurements
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.
A Universal Variance Reduction-Based Catalyst for Nonconvex Low-Rank Matrix Recovery
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery.
A Unified Framework for Low-Rank plus Sparse Matrix Recovery
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.
Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimizations
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.
Robust Wirtinger Flow for Phase Retrieval with Arbitrary Corruption
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.
Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization
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.
A Unified Variance Reduction-Based Framework for Nonconvex Low-Rank Matrix Recovery
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery.
Robust Gaussian Graphical Model Estimation with Arbitrary Corruption
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.
High-Dimensional Variance-Reduced Stochastic Gradient Expectation-Maximization Algorithm
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.
Uncertainty Assessment and False Discovery Rate Control in High-Dimensional Granger Causal Inference
Causal inference among high-dimensional time series data proves an important research problem in many fields.
Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimization
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.
Saving Gradient and Negative Curvature Computations: Finding Local Minima More Efficiently
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.
Third-order Smoothness Helps: Even Faster Stochastic Optimization Algorithms for Finding Local Minima
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.
Stochastic Variance-Reduced Hamilton Monte Carlo Methods
We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution.
Stochastic Variance-Reduced Cubic Regularized Newton Method
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.
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow
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.
Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks
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.
Learning One-hidden-layer ReLU Networks via Gradient Descent
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.
Stochastic Nested Variance Reduction for Nonconvex Optimization
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions.
Finding Local Minima via Stochastic Nested Variance Reduction
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.
A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery
We propose a primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery.
Covariate Adjusted Precision Matrix Estimation via Nonconvex Optimization
We propose a nonconvex estimator for the covariate adjusted precision matrix estimation problem in the high dimensional regime, under sparsity constraints.
Continuous and Discrete-time Accelerated Stochastic Mirror Descent for Strongly Convex Functions
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.
On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization
In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad.
Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks
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.
A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks
Depending on how much information an adversary can access to, adversarial attacks can be classified as white-box attack and black-box attack.
Sample Efficient Stochastic Variance-Reduced Cubic Regularization Method
The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods.
Third-order Smoothness Helps: Faster Stochastic Optimization Algorithms for Finding Local Minima
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.
Distributed Learning without Distress: Privacy-Preserving Empirical Risk Minimization
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.
Stochastic Nested Variance Reduced Gradient Descent for Nonconvex Optimization
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions.
Lower Bounds for Smooth Nonconvex Finite-Sum Optimization
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).
Stochastic Recursive Variance-Reduced Cubic Regularization Methods
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.
Generalization Error Bounds of Gradient Descent for Learning Over-parameterized Deep ReLU Networks
However, existing generalization error bounds are unable to explain the good generalization performance of over-parameterized DNNs.
An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradient
We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning.
Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks
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.
An Improved Analysis of Training Over-parameterized Deep Neural Networks
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.
DP-LSSGD: A Stochastic Optimization Method to Lift the Utility in Privacy-Preserving ERM
At the core of DP-LSSGD is the Laplacian smoothing, which smooths out the Gaussian noise used in the Gaussian mechanism.
A Knowledge Transfer Framework for Differentially Private Sparse Learning
We study the problem of estimating high dimensional models with underlying sparse structures while preserving the privacy of each training example.
Sample Efficient Policy Gradient Methods with Recursive Variance Reduction
Improving the sample efficiency in reinforcement learning has been a long-standing research problem.
NeuralUCB: Contextual Bandits with Neural Network-Based Exploration
To the best of our knowledge, our algorithm is the first neural network-based contextual bandit algorithm with near-optimal regret guarantee.
Training Deep Neural Networks with Partially Adaptive Momentum
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.
On the Dynamics and Convergence of Weight Normalization for Training Neural Networks
We present a proof of convergence for ReLU networks trained with weight normalization.
Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual Networks
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.
Efficient Privacy-Preserving Stochastic Nonconvex Optimization
While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge.
Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo
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.
Neural Contextual Bandits with UCB-based Exploration
To the best of our knowledge, it is the first neural network-based contextual bandit algorithm with a near-optimal regret guarantee.
Tight Sample Complexity of Learning One-hidden-layer Convolutional Neural Networks
We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters.
Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks
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.
How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?
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.
Stochastic Gradient Hamiltonian Monte Carlo Methods with Recursive Variance Reduction
Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) algorithms have received increasing attention in both theory and practice.
Rank Aggregation via Heterogeneous Thurstone Preference Models
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.
Towards Understanding the Spectral Bias of Deep Learning
An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions.
A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation
Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms.
A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks
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.
Double Explore-then-Commit: Asymptotic Optimality and Beyond
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.
Understanding the Intrinsic Robustness of Image Distributions using Conditional Generative Models
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.
On the Global Convergence of Training Deep Linear ResNets
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.
MOTS: Minimax Optimal Thompson Sampling
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.
Improving Adversarial Robustness Requires Revisiting Misclassified Examples
In this paper, we investigate the distinctive influence of misclassified and correctly classified examples on the final robustness of adversarial training.
Differentially Private Federated Learning with Laplacian Smoothing
Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users.
Improving Neural Language Generation with Spectrum Control
Recent Transformer-based models such as Transformer-XL and BERT have achieved huge success on various natural language processing tasks.
A Finite Time Analysis of Two Time-Scale Actor Critic Methods
In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i. i. d.
Revisiting Membership Inference Under Realistic Assumptions
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.
Agnostic Learning of a Single Neuron with Gradient Descent
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.
Optimization Theory for ReLU Neural Networks Trained with Normalization Layers
The success of deep neural networks is in part due to the use of normalization layers.
Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping
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.
RayS: A Ray Searching Method for Hard-label Adversarial Attack
Deep neural networks are vulnerable to adversarial attacks.
Ranked #1 on
Hard-label Attack
on MNIST
Nearly Minimax Optimal Reinforcement Learning for Discounted MDPs
We study the reinforcement learning problem for discounted Markov Decision Processes (MDPs) under the tabular setting.
Agnostic Learning of Halfspaces with Gradient Descent via Soft Margins
We analyze the properties of gradient descent on convex surrogates for the zero-one loss for the agnostic learning of linear halfspaces.
Neural Thompson Sampling
Thompson Sampling (TS) is one of the most effective algorithms for solving contextual multi-armed bandit problems.
Efficient Robust Training via Backward Smoothing
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.
Do Wider Neural Networks Really Help Adversarial Robustness?
Previous empirical results suggest that adversarial training requires wider networks for better performances.
Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling
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.
Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate
Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory.
Provable Multi-Objective Reinforcement Learning with Generative Models
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.
Logarithmic Regret for Reinforcement Learning with Linear Function Approximation
Reinforcement learning (RL) with linear function approximation has received increasing attention recently.
A Finite-Time Analysis of Two Time-Scale Actor-Critic Methods
In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i. i. d.
Neural Contextual Bandits with Deep Representation and Shallow Exploration
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.
Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes
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.
Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise
We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization.
Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints
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.
Almost Optimal Algorithms for Two-player Zero-Sum Linear Mixture Markov Games
To assess the optimality of our algorithm, we also prove an $\tilde{\Omega}( dH\sqrt{T})$ lower bound on the regret.
Nearly Minimax Optimal Regret for Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation
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.
Near-optimal Policy Optimization Algorithms for Learning Adversarial Linear Mixture MDPs
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.
Batched Neural Bandits
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.
Benign Overfitting of Constant-Stepsize SGD for Linear Regression
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).
Provable Robustness of Adversarial Training for Learning Halfspaces with Noise
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.
Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures
In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifier for linear classification problems.
Variance-reduced First-order Meta-learning for Natural Language Processing Tasks
The core of our algorithm is to introduce a novel variance reduction term to the gradient estimation when performing the task adaptation.
Provably Efficient Representation Selection in Low-rank Markov Decision Processes: From Online to Offline RL
For the offline counterpart, ReLEX-LCB, we show that the algorithm can find the optimal policy if the representation class can cover the state-action space and achieves gap-dependent sample complexity.
Variance-Aware Off-Policy Evaluation with Linear Function Approximation
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.
Uniform-PAC Bounds for Reinforcement Learning with Linear Function Approximation
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.
Pure Exploration in Kernel and Neural Bandits
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.
Proxy Convexity: A Unified Framework for the Analysis of Neural Networks Trained by Gradient Descent
We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities.
Self-training Converts Weak Learners to Strong Learners in Mixture Models
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.
The Benefits of Implicit Regularization from SGD in Least Squares Problems
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.
Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization
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.
Iterative Teacher-Aware Learning
Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works.
Exploring Architectural Ingredients of Adversarially Robust Deep Neural Networks
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.
Adaptive Sampling for Heterogeneous Rank Aggregation from Noisy Pairwise Comparisons
In heterogeneous rank aggregation problems, users often exhibit various accuracy levels when comparing pairs of items.
Last Iterate Risk Bounds of SGD with Decaying Stepsize for Overparameterized Linear Regression
In this paper, we provide a problem-dependent analysis on the last iterate risk bounds of SGD with decaying stepsize, for (overparameterized) linear regression problems.
Reward-Free Model-Based Reinforcement Learning with Linear Function Approximation
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.
Model-based Reinforcement Learning
reinforcement-learning
+1
Adaptive Differentially Private Empirical Risk Minimization
We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization.
Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes
To the best of our knowledge, this is the first provable privacy-preserving RL algorithm with linear function approximation.
Faster Perturbed Stochastic Gradient Methods for Finding Local Minima
In this paper, we propose LENA (Last stEp shriNkAge), a faster perturbed stochastic gradient framework for finding local minima.
Learning Stochastic Shortest Path with Linear Function Approximation
To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP.
Linear Contextual Bandits with Adversarial Corruptions
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.
On the Convergence and Robustness of Adversarial Training
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.
Benign Overfitting in Adversarially Robust Linear Classification
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.
Learning Neural Contextual Bandits Through Perturbed Rewards
Thanks to the power of representation learning, neural contextual bandit algorithms demonstrate remarkable performance improvement against their classical counterparts.
Benign Overfitting in Two-layer Convolutional Neural Networks
In this paper, we study the benign overfitting phenomenon in training a two-layer convolutional neural network (CNN).
Optimal Online Generalized Linear Regression with Stochastic Noise and Its Application to Heteroscedastic Bandits
We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise.
Risk Bounds of Multi-Pass SGD for Least Squares in the Interpolation Regime
Stochastic gradient descent (SGD) has achieved great success due to its superior performance in both optimization and generalization.
On the Convergence of Certified Robust Training with Interval Bound Propagation
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.
Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions
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.
Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPs
When applying our weighted least square estimator to heterogeneous linear bandits, we can obtain an $\tilde O(d\sqrt{\sum_{k=1}^K \sigma_k^2} +d)$ regret in the first $K$ rounds, where $d$ is the dimension of the context and $\sigma_k^2$ is the variance of the reward in the $k$-th round.
A Simple and Provably Efficient Algorithm for Asynchronous Federated Contextual Linear Bandits
To the best of our knowledge, this is the first provably efficient algorithm that allows fully asynchronous communication for federated contextual linear bandits, while achieving the same regret guarantee as in the single-agent setting.
The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift
Our bounds suggest that for a large class of linear regression instances, transfer learning with $O(N^2)$ source data (and scarce or no target data) is as effective as supervised learning with $N$ target data.
Towards Understanding Mixture of Experts in Deep Learning
To our knowledge, this is the first result towards formally understanding the mechanism of the MoE layer for deep learning.
Learning Two-Player Mixture Markov Games: Kernel Function Approximation and Correlated Equilibrium
We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS).
A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning
With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL).
Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization
AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.
Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes
In this paper, we consider the contextual bandit with general function approximation and propose a computationally efficient algorithm to achieve a regret of $\tilde{O}(\sqrt{T}+\zeta)$.
Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes
We study reinforcement learning (RL) with linear function approximation.
Structure-informed Language Models Are Protein Designers
This paper demonstrates that language models are strong structure-based protein designers.
Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency
We propose a variance-adaptive algorithm for linear mixture MDPs, which achieves a problem-dependent horizon-free regret bound that can gracefully reduce to a nearly constant regret for deterministic MDPs.
Finite-Sample Analysis of Learning High-Dimensional Single ReLU Neuron
On the other hand, we provide some negative results for stochastic gradient descent (SGD) for ReLU regression with symmetric Bernoulli data: if the model is well-specified, the excess risk of SGD is provably no better than that of GLM-tron ignoring constant factors, for each problem instance; and in the noiseless case, GLM-tron can achieve a small risk while SGD unavoidably suffers from a constant risk in expectation.
Benign Overfitting for Two-layer ReLU Convolutional Neural Networks
We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk.
The Benefits of Mixup for Feature Learning
We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data).
Borda Regret Minimization for Generalized Linear Dueling Bandits
To attain this lower bound, we propose an explore-then-commit type algorithm for the stochastic setting, which has a nearly matching regret upper bound $\tilde{O}(d^{2/3} T^{2/3})$.
On the Interplay Between Misspecification and Sub-optimality Gap in Linear Contextual Bandits
We show that, when the misspecification level $\zeta$ is dominated by $\tilde O (\Delta / \sqrt{d})$ with $\Delta$ being the minimal sub-optimality gap and $d$ being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound $\tilde O (d^2/\Delta)$ as in the well-specified setting up to logarithmic factors.
Optimal Horizon-Free Reward-Free Exploration for Linear Mixture MDPs
The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is "horizon-free".
Personalized Federated Learning under Mixture of Distributions
The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy.
Cooperative Multi-Agent Reinforcement Learning: Asynchronous Communication and Linear Function Approximation
We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where multiple agents cooperate via communication through a central server.
Uniform-PAC Guarantees for Model-Based RL with Bounded Eluder Dimension
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation.
Horizon-free Reinforcement Learning in Adversarial Linear Mixture MDPs
Recent studies have shown that episodic reinforcement learning (RL) is no harder than bandits when the total reward is bounded by $1$, and proved regret bounds that have a polylogarithmic dependence on the planning horizon $H$.
Domain Specialization as the Key to Make Large Language Models Disruptive: A Comprehensive Survey
In this article, we present a comprehensive survey on domain specification techniques for large language models, an emerging direction critical for large language model applications.
The Implicit Bias of Batch Normalization in Linear Models and Two-layer Linear Convolutional Neural Networks
We show that when learning a linear model with batch normalization for binary classification, gradient descent converges to a uniform margin classifier on the training data with an $\exp(-\Omega(\log^2 t))$ convergence rate.
Diffusion Language Models Can Perform Many Tasks with Scaling and Instruction-Finetuning
We then reprogram pretrained masked language models into diffusion language models via diffusive adaptation, wherein task-specific finetuning and instruction finetuning are explored to unlock their versatility in solving general language tasks.
Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP
Multi-modal learning has become increasingly popular due to its ability to leverage information from different data sources (e. g., text and images) to improve the model performance.
Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning
However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees.
Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits
Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems.
How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?
Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters.
Pure Exploration in Asynchronous Federated Bandits
We study the federated pure exploration problem of multi-armed bandits and linear bandits, where $M$ agents cooperatively identify the best arm via communicating with the central server.
Corruption-Robust Offline Reinforcement Learning with General Function Approximation
Notably, under the assumption of single policy coverage and the knowledge of $\zeta$, our proposed algorithm achieves a suboptimality bound that is worsened by an additive factor of $\mathcal{O}(\zeta (C(\widehat{\mathcal{F}},\mu)n)^{-1})$ due to the corruption.
Rephrase and Respond: Let Large Language Models Ask Better Questions for Themselves
While it is widely acknowledged that the quality of a prompt, such as a question, significantly impacts the quality of the response provided by LLMs, a systematic method for crafting questions that LLMs can better comprehend is still underdeveloped.
Risk Bounds of Accelerated SGD for Overparameterized Linear Regression
Additionally, when our analysis is specialized to linear regression in the strongly convex setting, it yields a tighter bound for bias error than the best-known result.
A Nearly Optimal and Low-Switching Algorithm for Reinforcement Learning with General Function Approximation
The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes.
Fast Sampling via De-randomization for Discrete Diffusion Models
Despite its success in continuous spaces, discrete diffusion models, which apply to domains such as texts and natural languages, remain under-studied and often suffer from slow generation speed.
Sparse PCA with Oracle Property
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.
Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models
In this paper, we delve into the prospect of growing a strong LLM out of a weak one without the need for acquiring additional human-annotated data.
TrustLLM: Trustworthiness in Large Language Models
This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions.
Mitigating Object Hallucination in Large Vision-Language Models via Classifier-Free Guidance
The advancement of Large Vision-Language Models (LVLMs) has increasingly highlighted the critical issue of their tendency to hallucinate non-existing objects in the images.
Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path
Our algorithm achieves an $\tilde{\mathcal O}(dB_*\sqrt{K})$ regret bound, where $d$ is the dimension of the feature mapping in the linear transition kernel, $B_*$ is the upper bound of the total cumulative cost for the optimal policy, and $K$ is the number of episodes.
Towards Robust Model-Based Reinforcement Learning Against Adversarial Corruption
We also prove a lower bound to show that the additive dependence on $C$ is optimal.
Model-based Reinforcement Learning
reinforcement-learning
+1
Reinforcement Learning from Human Feedback with Active Queries
Aligning large language models (LLM) with human preference plays a key role in building modern generative models and can be achieved by reinforcement learning from human feedback (RLHF).
Self-Play Fine-Tuning of Diffusion Models for Text-to-Image Generation
Fine-tuning Diffusion Models remains an underexplored frontier in generative artificial intelligence (GenAI), especially when compared with the remarkable progress made in fine-tuning Large Language Models (LLMs).
DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design
Designing 3D ligands within a target binding site is a fundamental task in drug discovery.
Diffusion Language Models Are Versatile Protein Learners
This paper introduces diffusion protein language model (DPLM), a versatile protein language model that demonstrates strong generative and predictive capabilities for protein sequences.
Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems
Real-world multi-agent systems are often dynamic and continuous, where the agents co-evolve and undergo changes in their trajectories and interactions over time.
DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization
DecompOpt presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering to the molecular grammar.
Protein Conformation Generation via Force-Guided SE(3) Diffusion Models
The conformational landscape of proteins is crucial to understanding their functionality in complex biological processes.
Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization
Antibody design, a crucial task with significant implications across various disciplines such as therapeutics and biology, presents considerable challenges due to its intricate nature.
Feel-Good Thompson Sampling for Contextual Dueling Bandits
In this paper, we propose a Thompson sampling algorithm, named FGTS. CDB, for linear contextual dueling bandits.
Settling Constant Regrets in Linear Markov Decision Processes
To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation for infinite runs without relying on prior distribution assumptions.
Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback
Learning from human feedback plays an important role in aligning generative models, such as large language models (LLM).
Padam: Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks
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.
