Study shows robust method for estimating density ratios even with heavy contamination.
problem Estimating density ratios in the presence of heavy contamination.
method Weighted density ratio estimation (DRE) with doubly strong robustness.
result Weighted DRE achieves sparse consistency under heavy contamination.
This work analyzes DP-SGD for online LDP problems with practical convergence rates.
problem Analyzing DP-SGD for online LDP problems with practical convergence rates.
method Developed a general framework for online LDP model in stochastic optimization problems, conducted non-asymptotic convergence analysis.
result Comprehensive non-asymptotic convergence analysis of the proposed estimators in finite-sample situations.
The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
Constructs non-asymptotic confidence regions for unknown functions in RKHS.
problem Global probabilistic confidence regions for unknown functions in RKHS.
method Reduces confidence region construction to estimating RKHS norm.
result Valid confidence regions can be constructed non-asymptotically.
New IRL algorithm identifies optimal reward and policy from expert demonstrations.
problem Understanding reward functions from expert demonstrations with neural networks.
method Two-timescale single-loop IRL algorithm for neural network parameterized rewards.
result First IRL algorithm with non-asymptotic convergence guarantee and global optimality in neural network settings.
We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i.e., establishing the rates of conve…
This study analyzes LTS in sparse models with finite sample error bounds.
problem Robust regression in high-dimensional sparse models with limited data.
method Non-asymptotic analysis of LTS error bounds.
result Established finite sample error bounds for LTS in sparse models.
New algorithm achieves near optimal sample complexity for 1-identification problem.
problem Determining if an arm's mean reward is at least a known threshold with high probability.
method Design of Sequential-Exploration-Exploitation (SEE) algorithm with non-asymptotic analysis.
result Achieves near optimality in sample complexity, matching upper and lower bounds up to a polynomial logarithmic factor.
This paper analyzes adaptive gradient algorithms for better performance in ill-conditioned problems.
problem Poor performance of standard stochastic gradient algorithms in ill-conditioned problems.
method Non-asymptotic analysis of adaptive gradient algorithms (Adagrad and Stochastic Newton) for strongly convex objectives.
result Theoretical analysis and adaptation to practical applications like linear regression and regularized GLM.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.
problem Training neural networks with ReLU activation.
method Non-asymptotic convergence analysis of SGHMC with discontinuous gradients.
result Explicit upper bounds for expected excess risk in non-convex optimization.
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
Study non-asymptotic BPI guarantees for online RL.
problem Identify optimal policy in MDP with high confidence.
method Non-asymptotic sample complexity guarantees for NaS algorithm.
result Sample complexity depends on MDP connectivity and curvature.
Simple bounds for covariance and Gram matrices across various settings.
problem Capturing the behavior of smaller eigenvalues in covariance and Gram matrices.
method General-purpose theorem converting uniform bounds into relative bounds.
result Sharper control of eigenvalues across the spectrum.
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
New algorithm reduces sample complexity for Top Two method.
problem Fixed-confidence best arm identification for Top Two methods.
method UCB-based Top Two algorithm for non-asymptotic analysis.
result First non-asymptotic upper bound on expected sample complexity.
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the afo…
Proof of Gaussian ML estimator consistency in linear auto-regressive models.
problem Consistency of Gaussian maximum likelihood estimator in linear auto-regressive models.
method Information-theoretic proof without stability assumptions.
result Nearly optimal non-asymptotic rates for parameter recovery.
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve O ( n − 1 / 2 ) O(n^{-1 / 2}) O ( n − 1/2 ) convergence rate under regularity assumptions. This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\wid…
VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.
problem Stochastic convex optimization under convex constraints.
method Natural variance reduced proximal gradient (VRPG) algorithm.
result VRPG achieves local minimax lower bound up to constants and log factor of N N N . Study spectral properties of graph Laplacian for manifold data.
problem Understanding spectral properties of graph Laplacian for manifold data.
method Non-asymptotic error bounds on spectral properties of empirical graph Laplacian.
result Eigenvalues and eigenspaces of empirical graph Laplacian are close to Laplace-Beltrami operator of manifold.
New analysis for learning and applying preconditioners in MCMC improves efficiency.
problem Improving efficiency of MCMC algorithms by modifying them with preconditioners.
method Analyzes and compares computational costs of MCMC schemes with and without preconditioners.
result Establishes non-asymptotic guarantees for MCMC algorithms that learn and use preconditioners.
Gradient-based temporal difference (GTD) algorithms are widely used in off-policy learning scenarios. Among them, the two time-scale TD with gradient correction (TDC) algorithm has been shown to have superior performance. In contrast to previous studies that characterized the non-asymptotic convergence rate of TDC only…
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
New methods improve temporal difference learning for policy evaluation in Markov decision processes.
problem Improving temporal difference learning for policy evaluation in Markov decision processes.
method Introduced variance-reduced forms of stochastic approximation to achieve non-asymptotic, instance-dependent optimality.
result Temporal difference learning is strictly suboptimal, but variance-reduced forms achieve optimality up to logarithmic factors.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
New framework predicts AMP behavior in spiked models for finite iterations.
problem Understanding AMP dynamics in high-dimensional spiked models.
method Developed a non-asymptotic framework for AMP in spiked matrix estimation.
result Predicted AMP behavior for up to O ( n p o l y log n ) O\big(\frac{n}{\mathrm{poly}\log n}\big) O ( poly l o g n n ) iterations in Z 2 \mathbb{Z}_2 Z 2 synchronization. Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.
problem Analyzing the sample complexity of two timescale reinforcement learning algorithms.
method Non-asymptotic analysis of linear and nonlinear TDC and Greedy-GQ algorithms under Markovian sampling with constant stepsize.
result The paper provides non-asymptotic convergence results for two timescale linear and nonlinear TDC and Greedy-GQ algorithms.
Analyzes learning and applying preconditioners in MCMC for efficiency.
problem Improving efficiency of MCMC algorithms.
method Non-asymptotic analysis of schemes that learn preconditioners.
result Established non-asymptotic guarantees for preconditioned ULA.
Develops a generalized version of Chung's Lemma for stochastic optimization methods.
problem Establishing asymptotic convergence rates for stochastic optimization methods under various step size rules.
method Generalized version of Chung's Lemma for a broader family of step size rules.
result Demonstrates tight non-asymptotic convergence rates for various stochastic methods.
Paper analyzes ensemble Kalman updates for effective dimension and localization.
problem Why small ensemble sizes work well in inverse problems and data assimilation.
method Non-asymptotic analysis of ensemble Kalman updates, focusing on effective dimension and localization.
result Rigorously explains why a small ensemble size is sufficient when prior covariance has moderate effective dimension.
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time T T T for multi-modal data distributions. Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O ( n − 1 / 4 ) \mathcal{O}(n^{-1/4}) O ( n − 1/4 ) convergence rates and guarantees consistent inference. Paper analyzes SVGD algorithm for non-asymptotic convergence.
problem Optimizing a set of particles to approximate a target probability distribution.
method Finite time analysis of SVGD algorithm, providing descent lemma and convergence rates.
result SVGD algorithm decreases the objective at each iteration and converges to the target distribution.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
A new strategy for identifying the best arm in Gaussian bandits with improved exploration.
problem Best-arm identification for Gaussian bandits with bounded means and unit variance.
method Exploration-Biased Sampling, a non-asymptotic approach with improved exploration behavior.
result Improved exploration behavior makes the strategy more stable and interpretable.
We analyze training dynamics in Gaussian mixture models using a comparison theorem.
problem Analyzing training algorithms with Gaussian mixture data.
method Applying a Gaussian comparison theorem to a specific family of training algorithms.
result Validated dynamic mean-field expressions and provided iterative refinement schemes.
New weighted Lasso estimates improve logistic regression performance with measurement error.
problem Improper Lasso estimates in sparse logistic regression with equal penalties.
method Proposed weighted Lasso estimates using McDiarmid inequality for non-asymptotic oracle inequalities.
result Finite sample behavior illustrated by non-asymptotic oracle inequalities for estimation and prediction errors.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.
problem Improving Bayesian algorithm performance through precise deviation bounds.
method Novel integral representation of Dirichlet sum density, Gaussian approximation, complex analysis.
result Significantly sharpened regret bounds for Multinomial Thompson Sampling.
This paper establishes non-asymptotic learning bounds for the DR covariate shift adaptation.
problem Distribution shift between training and test domains in machine learning.
method Doubly-robust (DR) estimator combining density ratio estimation and pilot regression model.
result First non-asymptotic learning bounds for DR covariate shift adaptation.
New method for semiparametric bandits reduces regret to optimal levels.
problem Complex reward structures in semiparametric bandits.
method Experimental-design approach with sharp regret bound and PAC bound.
result Minimax regret of i l d e O ( d T ) ilde{O}(\sqrt{dT}) i l d e O ( d T ) and logarithmic regret under positive suboptimality gap. Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significan…
The paper analyzes the training dynamics of a transformer for next-token prediction.
problem Understanding the non-asymptotic performance of transformers in next-token prediction.
method Characterizes training dataset properties, designs a two-stage training algorithm, and analyzes attention gradient properties.
result Trained transformers converge sub-linearly to max-margin solutions and exhibit linear convergence in cross-entropy loss.