Search Results for author:
Found 111 papers, 16 papers with code
Horizon-Free Regret for Linear Markov Decision Processes
A recent line of works showed regret bounds in reinforcement learning (RL) can be (nearly) independent of planning horizon, a. k. a.~the horizon-free bounds.
Transferable Reinforcement Learning via Generalized Occupancy Models
In this work, we propose a novel class of models - generalized occupancy models (GOMs) - that retain the generality of model-based RL while avoiding compounding error.
Reflect-RL: Two-Player Online RL Fine-Tuning for LMs
We propose Reflect-RL, a two-player system to fine-tune an LM using online RL, where a frozen reflection model assists the policy model.
Learning Optimal Tax Design in Nonatomic Congestion Games
We study how to learn the optimal tax design to maximize the efficiency in nonatomic congestion games.
Refined Sample Complexity for Markov Games with Independent Linear Function Approximation
Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL).
An Experimental Design Framework for Label-Efficient Supervised Finetuning of Large Language Models
To mitigate the annotation cost of SFT and circumvent the computational bottlenecks of active learning, we propose using experimental design.
Optimal Multi-Distribution Learning
Focusing on a hypothesis class of Vapnik-Chervonenkis (VC) dimension $d$, we propose a novel algorithm that yields an $varepsilon$-optimal randomized hypothesis with a sample complexity on the order of $(d+k)/\varepsilon^2$ (modulo some logarithmic factor), matching the best-known lower bound.
Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking
Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy.
Unleashing the Power of Pre-trained Language Models for Offline Reinforcement Learning
Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets.
How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and Initialization
This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from $\Omega (1/T^2)$ to linear convergence.
Settling the Sample Complexity of Online Reinforcement Learning
While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a ``large-sample'' regime, imposing enormous burn-in cost in order for their algorithms to operate optimally.
A Black-box Approach for Non-stationary Multi-agent Reinforcement Learning
Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges.
Improved Active Multi-Task Representation Learning via Lasso
In addition to our sample complexity results, we also characterize the potential of our $\nu^1$-based strategy in sample-cost-sensitive settings.
Over-Parameterization Exponentially Slows Down Gradient Descent for Learning a Single Neuron
This is the first global convergence result for this problem beyond the exact-parameterization setting ($n=1$) in which the gradient descent enjoys an $\exp(-\Omega(T))$ rate.
Breaking the Curse of Multiagents in a Large State Space: RL in Markov Games with Independent Linear Function Approximation
In contrast, existing works for Markov games with function approximation have sample complexity bounds scale with the size of the \emph{joint action space} when specialized to the canonical tabular Markov game setting, which is exponentially large in the number of agents.
A Reduction-based Framework for Sequential Decision Making with Delayed Feedback
We study stochastic delayed feedback in general multi-agent sequential decision making, which includes bandits, single-agent Markov decision processes (MDPs), and Markov games (MGs).
Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments
We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule.
Understanding Incremental Learning of Gradient Descent: A Fine-grained Analysis of Matrix Sensing
It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models.
Offline congestion games: How feedback type affects data coverage requirement
Starting from the facility-level (a. k. a., semi-bandit) feedback, we propose a novel one-unit deviation coverage condition and give a pessimism-type algorithm that can recover an approximate NE.
Horizon-Free and Variance-Dependent Reinforcement Learning for Latent Markov Decision Processes
We complement our positive result with a novel $\Omega(\sqrt{\mathsf{Var}^\star M S A K})$ regret lower bound with $\Gamma = 2$, which shows our upper bound minimax optimal when $\Gamma$ is a constant for the class of variance-bounded LMDPs.
On the Power of Pre-training for Generalization in RL: Provable Benefits and Hardness
Generalization in Reinforcement Learning (RL) aims to learn an agent during training that generalizes to the target environment.
Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies
We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class.
Faster Last-iterate Convergence of Policy Optimization in Zero-Sum Markov Games
Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to interact in a shared dynamic environment -- permeates across a wide range of critical applications.
Blessing of Class Diversity in Pre-training
Here, $n$ is the number of pre-training data and $m$ is the number of data in the downstream task, and typically $n \gg m$.
Denoised MDPs: Learning World Models Better Than the World Itself
The ability to separate signal from noise, and reason with clean abstractions, is critical to intelligence.
Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization
We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $\min_{\mathbf{x}}\max_{\mathbf{y}}~F(\mathbf{x}) + H(\mathbf{x},\mathbf{y}) - G(\mathbf{y})$, where one has access to stochastic first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$.
Learning in Congestion Games with Bandit Feedback
We propose a centralized algorithm for Markov congestion games, whose sample complexity again has only polynomial dependence on all relevant problem parameters, but not the size of the action set.
On Gap-dependent Bounds for Offline Reinforcement Learning
This paper presents a systematic study on gap-dependent sample complexity in offline reinforcement learning.
Provably Efficient Offline Multi-agent Reinforcement Learning via Strategy-wise Bonus
Furthermore, for offline multi-agent general-sum Markov games, based on the strategy-wise bonus and a novel surrogate function, we give the first algorithm whose sample complexity only scales $\sum_{i=1}^mA_i$ where $A_i$ is the action size of the $i$-th player and $m$ is the number of players.
Multi-agent Reinforcement Learning
reinforcement-learning
+1
Provable General Function Class Representation Learning in Multitask Bandits and MDPs
While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited.
Variance-Aware Sparse Linear Bandits
On the other hand, in the benign setting where there is no noise and the action set is the unit sphere, one can use divide-and-conquer to achieve $\widetilde{\mathcal O}(1)$ regret, which is (nearly) independent of $d$ and $T$.
Nearly Minimax Algorithms for Linear Bandits with Shared Representation
We give novel algorithms for multi-task and lifelong linear bandits with shared representation.
Horizon-Free Reinforcement Learning in Polynomial Time: the Power of Stationary Policies
This paper gives the first polynomial-time algorithm for tabular Markov Decision Processes (MDP) that enjoys a regret bound \emph{independent on the planning horizon}.
Understanding Curriculum Learning in Policy Optimization for Online Combinatorial Optimization
Furthermore, our theory explains the benefit of curriculum learning: it can find a strong sampling policy and reduce the distribution shift, a critical quantity that governs the convergence rate in our theorem.
TransFollower: Long-Sequence Car-Following Trajectory Prediction through Transformer
Through cross-attention between encoder and decoder, the decoder learns to build a connection between historical driving and future LV speed, based on which a prediction of future FV speed can be obtained.
Active Multi-Task Representation Learning
To leverage the power of big data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications.
Reward-Free RL is No Harder Than Reward-Aware RL in Linear Markov Decision Processes
We first develop a computationally efficient algorithm for reward-free RL in a $d$-dimensional linear MDP with sample complexity scaling as $\widetilde{\mathcal{O}}(d^2 H^5/\epsilon^2)$.
When is Offline Two-Player Zero-Sum Markov Game Solvable?
We study what dataset assumption permits solving offline two-player zero-sum Markov games.
Multi-agent Reinforcement Learning
reinforcement-learning
+2
Nearly Optimal Policy Optimization with Stable at Any Time Guarantee
Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms.
First-Order Regret in Reinforcement Learning with Linear Function Approximation: A Robust Estimation Approach
Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making.
Towards Demystifying Representation Learning with Non-contrastive Self-supervision
Non-contrastive methods of self-supervised learning (such as BYOL and SimSiam) learn representations by minimizing the distance between two views of the same image.
Gap-Dependent Bounds for Two-Player Markov Games
As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention.
Global Convergence of Gradient Descent for Asymmetric Low-Rank Matrix Factorization
We study the asymmetric low-rank factorization problem: \[\min_{\mathbf{U} \in \mathbb{R}^{m \times d}, \mathbf{V} \in \mathbb{R}^{n \times d}} \frac{1}{2}\|\mathbf{U}\mathbf{V}^\top -\mathbf{\Sigma}\|_F^2\] where $\mathbf{\Sigma}$ is a given matrix of size $m \times n$ and rank $d$.
A Reduction-Based Framework for Conservative Bandits and Reinforcement Learning
We also obtain a new upper bound for conservative low-rank MDP.
Corruption Robust Active Learning
We conduct theoretical studies on streaming-based active learning for binary classification under unknown adversarial label corruptions.
On the Power of Multitask Representation Learning in Linear MDP
We first discover a \emph{Least-Activated-Feature-Abundance} (LAFA) criterion, denoted as $\kappa$, with which we prove that a straightforward least-square algorithm learns a policy which is $\tilde{O}(H^2\sqrt{\frac{\mathcal{C}(\Phi)^2 \kappa d}{NT}+\frac{\kappa d}{n}})$ sub-optimal.
Provable Adaptation across Multiway Domains via Representation Learning
This paper studies zero-shot domain adaptation where each domain is indexed on a multi-dimensional array, and we only have data from a small subset of domains.
Stochastic Shortest Path: Minimax, Parameter-Free and Towards Horizon-Free Regret
We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state.
Nearly Horizon-Free Offline Reinforcement Learning
To the best of our knowledge, these are the \emph{first} set of nearly horizon-free bounds for episodic time-homogeneous offline tabular MDP and linear MDP with anchor points.
Bilinear Classes: A Structural Framework for Provable Generalization in RL
The framework incorporates nearly all existing models in which a polynomial sample complexity is achievable, and, notably, also includes new models, such as the Linear $Q^*/V^*$ model in which both the optimal $Q$-function and the optimal $V$-function are linear in some known feature space.
Near-Optimal Randomized Exploration for Tabular Markov Decision Processes
To achieve the desired result, we develop 1) a new clipping operation to ensure both the probability of being optimistic and the probability of being pessimistic are lower bounded by a constant, and 2) a new recursive formula for the absolute value of estimation errors to analyze the regret.
Provably Efficient Policy Optimization for Two-Player Zero-Sum Markov Games
Policy-based methods with function approximation are widely used for solving two-player zero-sum games with large state and/or action spaces.
Improved Corruption Robust Algorithms for Episodic Reinforcement Learning
We study episodic reinforcement learning under unknown adversarial corruptions in both the rewards and the transition probabilities of the underlying system.
Fine-Grained Gap-Dependent Bounds for Tabular MDPs via Adaptive Multi-Step Bootstrap
We further show that for general MDPs, AMB suffers an additional $\frac{|Z_{mul}|}{\Delta_{min}}$ regret, where $Z_{mul}$ is the set of state-action pairs $(s, a)$'s satisfying $a$ is a non-unique optimal action for $s$.
Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDP
With the new confidence sets, we obtain the follow regret bounds: For linear bandits, we obtain an $\tilde{O}(poly(d)\sqrt{1 + \sum_{k=1}^{K}\sigma_k^2})$ data-dependent regret bound, where $d$ is the feature dimension, $K$ is the number of rounds, and $\sigma_k^2$ is the \emph{unknown} variance of the reward at the $k$-th round.
A Provably Efficient Algorithm for Linear Markov Decision Process with Low Switching Cost
This paper focuses on the linear Markov Decision Process (MDP) recently studied in [Yang et al 2019, Jin et al 2020] where the linear function approximation is used for generalization on the large state space.
Planning with General Objective Functions: Going Beyond Total Rewards
Standard sequential decision-making paradigms aim to maximize the cumulative reward when interacting with the unknown environment., i. e., maximize $\sum_{h = 1}^H r_h$ where $H$ is the planning horizon.
Agnostic $Q$-learning with Function Approximation in Deterministic Systems: Near-Optimal Bounds on Approximation Error and Sample Complexity
The current paper studies the problem of agnostic $Q$-learning with function approximation in deterministic systems where the optimal $Q$-function is approximable by a function in the class $\mathcal{F}$ with approximation error $\delta \ge 0$.
Is Long Horizon RL More Difficult Than Short Horizon RL?
In a COLT 2018 open problem, Jiang and Agarwal conjectured that, for tabular, episodic reinforcement learning problems, there exists a sample complexity lower bound which exhibits a polynomial dependence on the horizon --- a conjecture which is consistent with all known sample complexity upper bounds.
Impact of Representation Learning in Linear Bandits
For the finite-action setting, we present a new algorithm which achieves $\widetilde{O}(T\sqrt{kN} + \sqrt{dkNT})$ regret, where $N$ is the number of rounds we play for each bandit.
Nearly Minimax Optimal Reward-free Reinforcement Learning
In the planning phase, the agent needs to return a near-optimal policy for arbitrary reward functions.
Is Reinforcement Learning More Difficult Than Bandits? A Near-optimal Algorithm Escaping the Curse of Horizon
Episodic reinforcement learning generalizes contextual bandits and is often perceived to be more difficult due to long planning horizon and unknown state-dependent transitions.
How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks
Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e. g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features.
On Reward-Free Reinforcement Learning with Linear Function Approximation
The sample complexity of our algorithm is polynomial in the feature dimension and the planning horizon, and is completely independent of the number of states and actions.
$Q$-learning with Logarithmic Regret
This paper presents the first non-asymptotic result showing that a model-free algorithm can achieve a logarithmic cumulative regret for episodic tabular reinforcement learning if there exists a strictly positive sub-optimality gap in the optimal $Q$-function.
When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems?
Though errors in past actions may affect the future, we are able to bound the number of particles needed so that the long-run reward of the policy based on particle filtering is close to that based on exact inference.
Is Long Horizon Reinforcement Learning More Difficult Than Short Horizon Reinforcement Learning?
Our analysis introduces two ideas: (i) the construction of an $\varepsilon$-net for optimal policies whose log-covering number scales only logarithmically with the planning horizon, and (ii) the Online Trajectory Synthesis algorithm, which adaptively evaluates all policies in a given policy class using sample complexity that scales with the log-covering number of the given policy class.
Provably Efficient Exploration for Reinforcement Learning Using Unsupervised Learning
Motivated by the prevailing paradigm of using unsupervised learning for efficient exploration in reinforcement learning (RL) problems [tang2017exploration, bellemare2016unifying], we investigate when this paradigm is provably efficient.
Provable Representation Learning for Imitation Learning via Bi-level Optimization
We formulate representation learning as a bi-level optimization problem where the "outer" optimization tries to learn the joint representation and the "inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters.
Few-Shot Learning via Learning the Representation, Provably
First, we study the setting where this common representation is low-dimensional and provide a fast rate of $O\left(\frac{\mathcal{C}\left(\Phi\right)}{n_1T} + \frac{k}{n_2}\right)$; here, $\Phi$ is the representation function class, $\mathcal{C}\left(\Phi\right)$ is its complexity measure, and $k$ is the dimension of the representation.
Agnostic Q-learning with Function Approximation in Deterministic Systems: Tight Bounds on Approximation Error and Sample Complexity
2) In conjunction with the lower bound in [Wen and Van Roy, NIPS 2013], our upper bound suggests that the sample complexity $\widetilde{\Theta}\left(\mathrm{dim}_E\right)$ is tight even in the agnostic setting.
Over-parameterized Adversarial Training: An Analysis Overcoming the Curse of Dimensionality
Our work proves convergence to low robust training loss for \emph{polynomial} width instead of exponential, under natural assumptions and with the ReLU activation.
Optimism in Reinforcement Learning with Generalized Linear Function Approximation
We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation.
Provably Efficient Q-learning with Function Approximation via Distribution Shift Error Checking Oracle
Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i. e, approximating Q-functions with linear functions, it is still an open problem how to design a provably efficient algorithm that learns a near-optimal policy.
Enhanced Convolutional Neural Tangent Kernels
An exact algorithm to compute CNTK (Arora et al., 2019) yielded the finding that classification accuracy of CNTK on CIFAR-10 is within 6-7% of that of that of the corresponding CNN architecture (best figure being around 78%) which is interesting performance for a fixed kernel.
Continuous Control with Contexts, Provably
To our knowledge, this is first provably efficient algorithm to build a decoder in the continuous control setting.
Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?
With regards to the statistical viewpoint, this question is largely unexplored, and the extant body of literature mainly focuses on conditions which permit sample efficient reinforcement learning with little understanding of what are necessary conditions for efficient reinforcement learning.
Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks
On VOC07 testbed for few-shot image classification tasks on ImageNet with transfer learning (Goyal et al., 2019), replacing the linear SVM currently used with a Convolutional NTK SVM consistently improves performance.
DualSMC: Tunneling Differentiable Filtering and Planning under Continuous POMDPs
A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty.
PROVABLY BENEFITS OF DEEP HIERARCHICAL RL
Modern complex sequential decision-making problem often both low-level policy and high-level planning.
Towards Understanding the Importance of Shortcut Connections in Residual Networks
We show, however, that gradient descent combined with proper normalization, avoids being trapped by the spurious local optimum, and converges to a global optimum in polynomial time, when the weight of the first layer is initialized at 0, and that of the second layer is initialized arbitrarily in a ball.
Provably Efficient $Q$-learning with Function Approximation via Distribution Shift Error Checking Oracle
Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i. e, approximating $Q$-functions with linear functions, it is still an open problem on how to design a provably efficient algorithm that learns a near-optimal policy.
Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels
While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs.
On Stationary-Point Hitting Time and Ergodicity of Stochastic Gradient Langevin Dynamics
In this paper, using intuitions from stochastic differential equations, we provide a direct analysis for the hitting times of SGLD to the first and second order stationary points.
On Exact Computation with an Infinitely Wide Neural Net
An attraction of such ideas is that a pure kernel-based method is used to capture the power of a fully-trained deep net of infinite width.
Global Convergence of Adaptive Gradient Methods for An Over-parameterized Neural Network
Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks.
Acceleration via Symplectic Discretization of High-Resolution Differential Equations
We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method.
Provably efficient RL with Rich Observations via Latent State Decoding
We study the exploration problem in episodic MDPs with rich observations generated from a small number of latent states.
Width Provably Matters in Optimization for Deep Linear Neural Networks
We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tilde\Omega (L \cdot r \cdot d_{\mathrm{out}} \cdot \kappa^3 )$, where $r$ and $\kappa$ are the rank and the condition number of the input data, and $d_{\mathrm{out}}$ is the output dimension, then gradient descent with Gaussian random initialization converges to a global minimum at a linear rate.
Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter characterization of training speed than recent papers, an explanation for why training a neural net with random labels leads to slower training, as originally observed in [Zhang et al. ICLR'17].
How Many Samples are Needed to Estimate a Convolutional Neural Network?
We show that for an $m$-dimensional convolutional filter with linear activation acting on a $d$-dimensional input, the sample complexity of achieving population prediction error of $\epsilon$ is $\widetilde{O(m/\epsilon^2)$, whereas the sample-complexity for its FNN counterpart is lower bounded by $\Omega(d/\epsilon^2)$ samples.
Gradient Descent Finds Global Minima of Deep Neural Networks
Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex.
Understanding the Acceleration Phenomenon via High-Resolution Differential Equations
We also show that these ODEs are more accurate surrogates for the underlying algorithms; in particular, they not only distinguish between NAG-SC and Polyak's heavy-ball method, but they allow the identification of a term that we refer to as "gradient correction" that is present in NAG-SC but not in the heavy-ball method and is responsible for the qualitative difference in convergence of the two methods.
Gradient Descent Provably Optimizes Over-parameterized Neural Networks
One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth.
Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced
Using a discretization argument, we analyze gradient descent with positive step size for the non-convex low-rank asymmetric matrix factorization problem without any regularization.
Robust Nonparametric Regression under Huber's $ε$-contamination Model
We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up to absolute constants over the H\"{o}lder function class with smoothness parameters smaller than or equal to 1.
How Many Samples are Needed to Estimate a Convolutional or Recurrent Neural Network?
It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural Network (FNN) counterparts, and consequently require fewer training examples to accurately estimate their parameters.
Improved Learning of One-hidden-layer Convolutional Neural Networks with Overlaps
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned.
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.
On the Power of Over-parametrization in Neural Networks with Quadratic Activation
We provide new theoretical insights on why over-parametrization is effective in learning neural networks.
Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems.
Linear Convergence of the Primal-Dual Gradient Method for Convex-Concave Saddle Point Problems without Strong Convexity
We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex.
Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima
We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i. e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_j\sigma(\mathbf{w}^T\mathbf{Z}_j)$, in which both the convolutional weights $\mathbf{w}$ and the output weights $\mathbf{a}$ are parameters to be learned.
When is a Convolutional Filter Easy To Learn?
We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches.
Gradient Descent Can Take Exponential Time to Escape Saddle Points
Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape.
Stochastic Variance Reduction Methods for Policy Evaluation
Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states' long-term value under a given policy.
Computationally Efficient Robust Estimation of Sparse Functionals
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions.
On the Power of Truncated SVD for General High-rank Matrix Estimation Problems
This observation leads to many interesting results on general high-rank matrix estimation problems, which we briefly summarize below ($A$ is an $n\times n$ high-rank PSD matrix and $A_k$ is the best rank-$k$ approximation of $A$): (1) High-rank matrix completion: By observing $\Omega(\frac{n\max\{\epsilon^{-4}, k^2\}\mu_0^2\|A\|_F^2\log n}{\sigma_{k+1}(A)^2})$ elements of $A$ where $\sigma_{k+1}\left(A\right)$ is the $\left(k+1\right)$-th singular value of $A$ and $\mu_0$ is the incoherence, the truncated SVD on a zero-filled matrix satisfies $\|\widehat{A}_k-A\|_F \leq (1+O(\epsilon))\|A-A_k\|_F$ with high probability.
Efficient Nonparametric Smoothness Estimation
Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators.
An Improved Gap-Dependency Analysis of the Noisy Power Method
We consider the noisy power method algorithm, which has wide applications in machine learning and statistics, especially those related to principal component analysis (PCA) under resource (communication, memory or privacy) constraints.
