We prove non-asymptotic lower bounds on the expectation of the maximum of independent Gaussian variables and the expectation of the maximum of independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…
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48 results for “non-asymptotic lower bound”
Non asymptotic estimation lower bounds for LTI state space models with Cramér-Rao and van Treesmath.ST
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
Detecting a planted submatrix in random matrices with non-asymptotic methods.
problem Detecting a planted submatrix in random matrices with non-zero entries.
method Established minimax lower bounds and derived optimal tests for distinguishing the null and alternative hypotheses.
result Non-asymptotic upper and lower bounds match for any configuration of matrix dimensions.
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 .
Non-asymptotic Optimal Prediction Error for Growing-dimensional Partially Functional Linear Modelsmath.ST
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.
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.
New algorithm reduces clustering cost in bandit feedback.
problem Discovering hidden groupings in stochastic bandit feedback.
method ACB algorithm for active clustering with non-asymptotic lower bound.
result ACB algorithm's budget matches lower bound in most regimes.
Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiencymath.ST
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
problem Estimating linear functionals from observational data in causal inference and bandit literature.
method Two-stage procedures that first estimate treatment effect function, then use it to estimate the linear functional.
result Proves non-asymptotic upper bounds on mean-squared error for two-stage procedures and shows instance-dependent optimality.
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
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 convergence rate under regularity assumptions.
Study optimal stopping for diffusion processes using data-driven methods.
problem Optimal stopping for diffusion processes under unknown conditions.
method Data-driven approach, deriving upper and lower bounds on simple and cumulative regret.
result Verified minimax optimality and improved convergence rates.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action , the learner receives information about the payoff of every action in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair (and may…
Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.
problem Efficient tensor decomposition for count data models.
method Rank-constrained maximum-likelihood estimator for tensor decomposition.
result Achieves multiway analysis with variance matching Cramér-Rao Lower Bound up to constants and logarithmic factors.
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.
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 and logarithmic regret under positive suboptimality gap.
The paper improves confidence set construction for statistical inference.
problem Constructing reliable confidence sets in statistical inference.
method Establishes a finite-sample bound using effective dimension and generalized self-concordance.
result Developed a confidence set adapted to optimization landscapes.
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may …
Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.
problem Approximately solving linear fixed point equations with Markovian data.
method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.
result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.
Optimal sequential testing for Markovian data with lower and upper bounds.
problem Sequential hypothesis testing for Markovian data.
method Non-asymptotic lower bounds and optimal test design.
result Optimal test matches lower bound asymptotically.
New algorithm achieves instance-optimality in decision making.
problem Develop adaptive algorithms for interactive decision making.
method Introduce Allocation-Estimation Coefficient (AEC) and develop algorithm.
result First non-asymptotic instance-optimal performance guarantees.
The paper provides non-asymptotic Edgeworth expansions for neural network outputs.
problem Approximating deviations of finite-width neural networks from their Gaussian limit.
method Multidimensional Edgeworth expansions of arbitrary order for neural network outputs.
result Established a bound on the total variation distance between neural network output and its Edgeworth approximation.
Improved heteroscedastic regression with machine learning techniques.
problem Estimating weights in heteroscedastic linear regression with varying noise.
method Alternating minimization with weighted least squares and pseudogradient descent.
result Achieved a tighter error bound for estimating weights.
This work creates a CS for non-negative heavy-tailed data with bounded mean.
problem Constructing a confidence sequence for non-negative heavy-tailed data with bounded mean.
method Non-parametric, non-asymptotic lower confidence sequence construction.
result The constructed CS is efficient and can be converted into a closed-interval CS.
We study sparse principal components analysis in the high-dimensional setting, where (the number of variables) can be much larger than (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an …
New tests detect communities in dense bipartite graphs with high accuracy.
problem Detecting communities in dense bipartite graphs with high accuracy.
method Non-asymptotic upper and lower bounds, novel minimax-optimal tests, hard-thresholded nonlinear statistics.
result Non-asymptotic upper and lower bounds match for any configuration of graph sizes.
Study examines Lasso performance in high-dimensional MoE models.
problem Estimating MoE models in high-dimensional settings with Lasso.
method Investigates SGMoE models with Lasso regularization under mild assumptions.
result Provides non-asymptotic bounds for Lasso regularization parameter.
Improved error bounds for Langevin MCMC with scaling.
problem Improving convergence rates of Langevin MCMC.
method Introducing scaling terms in underdamped Langevin equation and analyzing conditions for improved error bounds.
result Appropriate scaling improves error bounds in terms of condition number.
We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with replacement, we focus here on popular but poorly-understood heuristics, which i…
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
Study gap-dependent regret bounds for risk-sensitive RL.
problem Risk-sensitive reinforcement learning with entropic risk measure.
method Propose cascaded gaps to adapt to problem structures, derive regret bounds.
result Exponential improvement over existing bounds in appropriate settings.
Study identifies change points in piecewise constant reward functions with fixed exploration budget.
problem Locating abrupt changes in piecewise constant reward functions under bandit feedback.
method Fixed exploration budget, piecewise constant bandit problem, lower bounds, near optimal algorithms.
result Established lower bounds and near matching upper bounds for both small and large budgets.
We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for whic…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum mean among a finite set of distributions compares to a given threshold. We deve…
This study improves estimation of the first principal component in multivariate functional data.
problem Estimating the first principal component of multivariate random processes.
method Defined covariance functions and operators, introduced LASSO optimization, and established minimax lower bounds.
result The method provides an optimal variance in the minimax sense for estimating eigenelements.
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 for multi-modal data distributions.
Study shows how discrete graph curvature relates to manifold curvature.
problem Relating discrete graph curvature to intrinsic manifold curvature.
method Continuum limits of Ollivier's Ricci curvature on data clouds.
result Random geometric graphs inherit global curvature properties of manifolds.
The paper studies reward concentration in MDPs, covering asymptotic and non-asymptotic settings.
problem Reward concentration in Markov Decision Processes (MDPs).
method Unified approach to reward concentration in MDPs, including asymptotic and non-asymptotic bounds.
result Rate-equivalent definitions of regret for learning policies.
Lower bounds on eigenspectrum show rich action spaces force polynomial regret in linear bandits.
problem Understanding the minimum eigenvalue growth in linear bandits with rich action sets.
method Non-asymptotic lower bound on eigenspectrum of design matrix.
result Minimum eigenvalue of expected design matrix grows as for sub-linear regret.
New oracles improve stochastic optimization with noisy or biased measurements.
problem Optimizing functions with noisy or biased measurements.
method Introduced biased gradient oracles for stochastic optimization, analyzed RSG and SGD algorithms with these oracles.
result Derived non-asymptotic bounds for convergence rates of algorithms with biased gradient oracles.
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.
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.
Simple method for estimating missing panel data entries with confidence intervals.
problem Estimating missing values in panel data with staggered adoption.
method Simple matrix algebra and singular value decomposition for estimation, with data-driven confidence intervals.
result Confidence intervals match non-asymptotic lower bounds, proving instance optimality.
Study best arm identification with limited precision sampling in bandits.
problem Limited precision sampling in multi-armed bandit problems.
method Proposed a modified tracking-based algorithm to handle non-unique optimal allocations and presented non-asymptotic bounds.
result Asymptotically optimal tracking-based algorithm for best arm identification.
Stabilizing Bandits using Regularization: Precise Regret and A Quantitative Central Limit Theoremstat.ML
Paper stabilizes bandit learning with regularization, improving inference under adaptive sampling.
problem Challenges in statistical inference with adaptive sampling.
method Refined stability condition for online algorithms, using regularized stochastic-mirror-descent-style methods.
result Derives precise regret bounds and asymptotic normality, showing necessity of regularization for valid inference.
Non-asymptotic tail bounds for Kostlan-Shub-Smale field on sphere
problem Estimating rank-R symmetric signal tensor from Gaussian observation
method Profile maximum likelihood estimator
result Finite-(k,d) error bound recovers asymptotically optimal rate
Optimizes shortfall risk using gradient-based methods.
problem Optimizing utility-based shortfall risk measures.
method Gradient-based stochastic optimization, non-asymptotic bounds derivation.
result Non-asymptotic convergence rate for optimizing UBSR.