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Found 33 papers, 3 papers with code
Optimal Statistical Guaratees for Adversarially Robust Gaussian Classification
In this paper, we provide the first result of the \emph{optimal} minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by \cite{schmidt2018adversarially}.
AC-EVAL: Evaluating Ancient Chinese Language Understanding in Large Language Models
Given the importance of ancient Chinese in capturing the essence of rich historical and cultural heritage, the rapid advancements in Large Language Models (LLMs) necessitate benchmarks that can effectively evaluate their understanding of ancient contexts.
Accelerating Convergence of Score-Based Diffusion Models, Provably
Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase.
Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models
Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties.
Towards a mathematical theory for consistency training in diffusion models
Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance.
A non-asymptotic distributional theory of approximate message passing for sparse and robust regression
Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension.
Federated Natural Policy Gradient Methods for Multi-task Reinforcement Learning
Federated reinforcement learning (RL) enables collaborative decision making of multiple distributed agents without sharing local data trajectories.
Query-aware Long Video Localization and Relation Discrimination for Deep Video Understanding
This model adeptly selects frames pertinent to queries, obviating the need for a complete movie-level knowledge graph.
Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling.
Sharp high-probability sample complexities for policy evaluation with linear function approximation
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes.
The Curious Price of Distributional Robustness in Reinforcement Learning with a Generative Model
Assuming access to a generative model that draws samples based on the nominal MDP, we characterize the sample complexity of RMDPs when the uncertainty set is specified via either the total variation (TV) distance or $\chi^2$ divergence.
Approximate message passing from random initialization with applications to $\mathbb{Z}_{2}$ synchronization
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations.
Minimax-Optimal Multi-Agent RL in Markov Games With a Generative Model
This paper studies multi-agent reinforcement learning in Markov games, with the goal of learning Nash equilibria or coarse correlated equilibria (CCE) sample-optimally.
A Non-Asymptotic Framework for Approximate Message Passing in Spiked Models
As two concrete consequences of the proposed analysis recipe: (i) when solving $\mathbb{Z}_2$ synchronization, we predict the behavior of spectrally initialized AMP for up to $O\big(\frac{n}{\mathrm{poly}\log n}\big)$ iterations, showing that the algorithm succeeds without the need of a subsequent refinement stage (as conjectured recently by \citet{celentano2021local}); (ii) we characterize the non-asymptotic behavior of AMP in sparse PCA (in the spiked Wigner model) for a broad range of signal-to-noise ratio.
Mitigating multiple descents: A model-agnostic framework for risk monotonization
Recent empirical and theoretical analyses of several commonly used prediction procedures reveal a peculiar risk behavior in high dimensions, referred to as double/multiple descent, in which the asymptotic risk is a non-monotonic function of the limiting aspect ratio of the number of features or parameters to the sample size.
Settling the Sample Complexity of Model-Based Offline Reinforcement Learning
We demonstrate that the model-based (or "plug-in") approach achieves minimax-optimal sample complexity without burn-in cost for tabular Markov decision processes (MDPs).
Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity
Offline or batch reinforcement learning seeks to learn a near-optimal policy using history data without active exploration of the environment.
Minimum $\ell_{1}$-norm interpolators: Precise asymptotics and multiple descent
An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful.
Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization
Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE) -- which are solutions to zero-sum two-player matrix games with entropy regularization -- at a linear rate.
Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting
The current paper pertains to a scenario with value-based linear representation, which postulates the linear realizability of the optimal Q-function (also called the "linear $Q^{\star}$ problem").
Softmax Policy Gradient Methods Can Take Exponential Time to Converge
The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning.
Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis
This paper addresses these questions for the synchronous setting: (1) when $|\mathcal{A}|=1$ (so that Q-learning reduces to TD learning), we prove that the sample complexity of TD learning is minimax optimal and scales as $\frac{|\mathcal{S}|}{(1-\gamma)^3\varepsilon^2}$ (up to log factor); (2) when $|\mathcal{A}|\geq 2$, we settle the sample complexity of Q-learning to be on the order of $\frac{|\mathcal{S}||\mathcal{A}|}{(1-\gamma)^4\varepsilon^2}$ (up to log factor).
Derandomizing Knockoffs
Model-X knockoffs is a general procedure that can leverage any feature importance measure to produce a variable selection algorithm, which discovers true effects while rigorously controlling the number or fraction of false positives.
Feature Importance
Variable Selection
Methodology
Applications
Debiasing Evaluations That are Biased by Evaluations
For example, universities ask students to rate the teaching quality of their instructors, and conference organizers ask authors of submissions to evaluate the quality of the reviews.
Randomized tests for high-dimensional regression: A more efficient and powerful solution
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$.
The Lasso with general Gaussian designs with applications to hypothesis testing
On the other hand, the Lasso estimator can be precisely characterized in the regime in which both $n$ and $p$ are large and $n/p$ is of order one.
Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization
This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization.
Sharp Statistical Guarantees for Adversarially Robust Gaussian Classification
In this paper, we provide the first result of the optimal minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by \cite{schmidt2018adversarially}.
Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction
Focusing on a $\gamma$-discounted MDP with state space $\mathcal{S}$ and action space $\mathcal{A}$, we demonstrate that the $\ell_{\infty}$-based sample complexity of classical asynchronous Q-learning --- namely, the number of samples needed to yield an entrywise $\varepsilon$-accurate estimate of the Q-function --- is at most on the order of $\frac{1}{\mu_{\min}(1-\gamma)^5\varepsilon^2}+ \frac{t_{mix}}{\mu_{\min}(1-\gamma)}$ up to some logarithmic factor, provided that a proper constant learning rate is adopted.
Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model
This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator).
Model-based Reinforcement Learning
Reinforcement Learning (RL)
Tackling small eigen-gaps: Fine-grained eigenvector estimation and inference under heteroscedastic noise
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i. e. the spacing between the associated eigenvalue and the rest of the spectrum) is particularly small; (2) how to perform estimation and inference on linear functionals of an eigenvector -- a sort of "fine-grained" statistical reasoning that goes far beyond the usual $\ell_2$ analysis.
Early stopping for kernel boosting algorithms: A general analysis with localized complexities
Early stopping of iterative algorithms is a widely-used form of regularization in statistics, commonly used in conjunction with boosting and related gradient-type algorithms.
Adaptive estimation of planar convex sets
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid.
Statistics Theory Statistics Theory
