This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.
problem Analyzing Greedy-GQ for reinforcement learning with Markovian noise.
method Develops finite-sample analysis for Greedy-GQ with linear function approximation under Markovian noise.
result Provides theoretical justification for choosing stepsizes for faster convergence.
The paper analyzes GTD algorithms with finite-sample bounds.
problem Convergence rate analysis of GTD family of algorithms.
method Formulated as stochastic gradient algorithms and analyzed using saddle-point error.
result Obtained finite-sample bounds on GTD performance.
New findings show modern neural networks have finite sample complexity in o-minimal structures.
problem Understanding the learnability of modern neural networks in a broad context.
method Analyzing feedforward neural networks definable in o-minimal structures.
result Modern neural networks, including MLPs, CNNs, GNNs, and transformers, have finite sample complexity in the agnostic PAC setting.
Estimates barycenter in geodesic spaces with finite sample bounds.
problem Estimating the barycenter of a distribution in geodesic spaces.
method Finite sample error bounds, Hoeffding- and Bernstein-type concentration inequalities, efficient algorithms.
result Statistical guarantees for efficient barycenter computation.
New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
problem Estimating causal effects with limited overlap in multivalued treatments.
method Stable Probability Weighting (SPW) and Finite-Sample Stable Probability Weighting (FPW) methods.
result SPW and FPW provide practical solutions for estimating and inferring causal effects with limited overlap.
Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents…
The paper shows how to learn causal representations with few environments and finite samples.
problem Learning causal representations from limited data and environments.
method Explicit, finite-sample guarantees with a logarithmic number of interventions.
result Consistent recovery of latent causal graph, mixing matrix, and unknown intervention targets.
Unified framework for finite-sample RL algorithms using Lyapunov theory.
problem Finite-sample convergence guarantees of asynchronous RL algorithms.
method Reformulate RL algorithms as Markovian SA, develop Lyapunov analysis.
result Mean-square error bounds and convergence for various RL algorithms.
Study non-parametric frequency-domain system identification from finite samples.
problem Frequency-domain system identification from limited data.
method Empirical Transfer Function Estimate (ETFE) under sub-Gaussian colored noise and stability assumptions.
result ETFE estimates are concentrated around true values with a finite-sample rate of N t o t − 1 / 3 N_{\mathrm{tot}}^{-1/3} N tot − 1/3 for all frequencies in the H ∞ \mathcal{H}_{\infty} H ∞ norm. The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.
problem Uncertainty in identifying density differences when supports overlap and densities have substantial pointwise differences.
method Analysis using the Poisson process and neural spike train decoding.
result The one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.
The paper analyzes off-policy TD-learning using generalized Bellman operators and provides finite-sample bounds.
problem High variance in off-policy TD-learning due to importance sampling.
method Derives finite-sample bounds for off-policy TD-like algorithms using generalized Bellman operators.
result First-known finite-sample guarantees for several off-policy TD algorithms.
The paper provides guarantees for high-dimensional DML estimators in observational studies.
problem Estimating treatment effects in observational settings with many covariates.
method Debiased machine learning (DML) with finite-sample guarantees.
result Bounding the deviation of finite-sample distribution from asymptotic Gaussian approximation.
This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
Proposes a method to create shorter, more accurate prediction intervals.
problem Challenges in achieving both conditional validity and interval efficiency in complex settings.
method Uses a conformal-style calibration method for neural network responses, adjusting to empirical PIT distribution.
result Demonstrates better conditional calibration and shorter intervals than existing methods.
Exact inference method for Wasserstein distance with finite-sample coverage.
problem Asymptotic approximation methods for Wasserstein distance lack finite-sample validity.
method Selective Inference inspired approach for exact inference.
result Valid confidence interval for Wasserstein distance with finite-sample coverage.
The paper studies how more data affects prediction risk in high-dimensional models.
problem The impact of increasing data on prediction risk in high-dimensional models.
method Derives central limit theorem and provides finite-sample distribution and confidence interval for prediction risk.
result Demonstrates 'more data hurt' phenomenon in high-dimensional least squares estimation.
We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k → ∞ k \to \infty k → ∞ as the sample size $n \to \in…
Improved mean estimation for symmetric distributions with finite-sample guarantees.
problem Estimating the mean of a symmetric distribution from samples.
method Using Fisher information rate for finite-sample guarantees.
result Finite-sample convergence close to subgaussian with variance 1/(n * I_r), where I_r is r-smoothed Fisher information.
Meta-learners improve causal effect estimation in small samples.
problem Estimating causal effects using machine learning methods.
method Sample-splitting and cross-fitting to reduce overfitting bias.
result Meta-learners' performance depends on sample size and estimation procedure.
Method constructs nonparametric prediction intervals with finite-sample guarantees.
problem Nonparametric instrumental variable regression with finite-sample coverage.
method Conformal inference framework applied to NPIV, combining with various estimators.
result Distribution-free, finite-sample coverage over chosen IV shifts.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
problem Understanding the effectiveness of tree-based methods in finite-sample settings, especially symbolic feature selection.
method Local ranking perspective, finite-sample analysis, oracle bounds, posterior contraction results, concordant divergence statistics.
result New insights and statistics for evaluating symbolic feature mappings.
MF-TRPO optimizes MFGs with finite sample guarantees.
problem Computing approximate Nash equilibria in MFGs.
method Extends TRPO to MFGs, providing convergence guarantees.
result Theoretical guarantees on MF-TRPO's convergence.
Correspondence found between exponential families and affine Grassmannians.
problem Understanding the relationship between exponential families and geometric structures.
method Established a one-to-one correspondence between exponential families and affine Grassmannians.
result Found a correspondence between minimal exponential families and affine Grassmannians.
New method uncovers zero entropy in dependent observations after finite samples.
problem Understanding uncertainty reduction in dependent observations.
method Minimum list entropy coupling, greedy algorithm.
result Zero entropy achieved with O(log(1/P_min)) samples for dependent observations.
New model-free DR-RL algorithm with finite sample complexity.
problem Limited model-free DR-RL methods with convergence guarantees or sample complexities.
method Integrates Multi-level Monte Carlo (MLMC) technique with threshold mechanism.
result First model-free DR-RL approach with finite sample complexity for total variation and Chi-square divergence.
Paper provides convergence guarantees for off-policy NAC with finite sample complexity.
problem Convergence analysis of off-policy natural actor-critic algorithm.
method Finite-sample analysis with Importance Sampling and Q-trace algorithm.
result Converges to global optimal policy with sample complexity O ( ε − 3 log 2 ( 1 / ε ) ) \mathcal{O}(ε^{-3}\log^2(1/ε)) O ( ε − 3 log 2 ( 1/ ε )) . Causal invariance can improve finite-sample domain adaptation, but only when the target risk margins are large.
problem Finite-sample domain adaptation
method Linear regression with causal knowledge
result Adaptive aggregation can match best candidate predictor while avoiding negative transfer
New method identifies parameters of wider shallow neural networks with biases.
problem Identifying parameters of wide shallow neural networks with biases from finite samples.
method Two-step pipeline: direction of weights via second order information, signs via algebraic evaluations, biases via gradient descent.
result Constructive methods and theoretical guarantees of finite sample identification for wider shallow networks with biases.
A theorem for debiasing machine learning with finite sample guarantees.
problem Calculating confidence intervals for machine learning functionals.
method Debiased machine learning based on bias correction and sample splitting.
result Nonasymptotic debiased machine learning theorem with finite sample guarantees.
Paper analyzes PSGLD for adaptive IRL with finite-sample bounds.
problem Estimating cost function of a forward learner using noisy gradients.
method Passive stochastic gradient Langevin dynamics (PSGLD) algorithm.
result Explicit bounds on 2-Wasserstein distance between PSGLD sample measure and stationary measure.
Estimates neural representation dimensionality from small sample sizes.
problem Estimating neural representation dimensionality from limited data.
method Proposed a bias-corrected estimator for participation ratio of eigenvalues.
result The estimator is more accurate with finite samples and noise.
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
Study bounds variance modulation function for K-spider distributions.
problem Bounding variance modulation function for K-spider distributions.
method Used folded moments and total probabilities of spider legs.
result Gave an interval for the variance modulation function.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
problem Learning polytrees with known skeleton structure.
method Proposes an efficient algorithm for learning d d d -polytrees in polynomial time and sample complexity when the skeleton is known. result Establishes finite-sample guarantees for efficient learning of d d d -polytrees. The paper introduces a frequency-domain estimator for low-order systems from noisy data.
problem Estimating frequency responses of low-order systems from noisy measurements.
method Uses a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint.
result Proves a finite-sample error bound and extends it to all frequencies through rational interpolation.
Study tests whether trade-off functions are above or below benchmarks using finite samples.
problem Testing trade-off functions between unknown distributions.
method Identifies a condition for nontrivial testing, constructs a test with error guarantees, and inverts the test for confidence bands.
result Finite-sample testing is possible under specific structural assumptions about rejection regions.
Split conformal prediction provides finite-sample guarantees for black-box models without distributional assumptions.
problem Weak performance guarantees for modern predictive models under minimal assumptions.
method Develops finite-sample guarantees for split conformal prediction, a method that uses nested prediction sets and order statistics.
result The coverage of prediction sets based on order statistics stochastically dominates the Beta distribution.
Deep learning method improves regression accuracy.
problem Nonparametric regression challenges.
method Over-parametrized deep neural networks with logistic activation, gradient descent, special topology, random initialization, and data-dependent learning rate.
result Theoretical bound on L 2 L_2 L 2 error and improved finite sample performance. Paper analyzes online tensorial ICA convergence with stochastic approximation.
problem Online tensorial ICA convergence analysis.
method Stochastic approximation for nonconvex optimization.
result Sharp finite-sample error bound of O ~ ( d / T ) \tilde{O}(\sqrt{d/T}) O ~ ( d / T ) . Moment polytope of toric exponential families is a projection of a simplex.
problem Understanding the geometry of exponential families in finite sample spaces.
method Toric torification and projection of higher-dimensional simplices.
result Moment polytope is a projection of a higher-dimensional simplex.
We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We t…
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.
Develops methods to adjust prediction set coverage based on post-selection analysis.
problem Adjusting prediction set coverage after initial analysis to better fit specific needs.
method Post-selection conformal inference to adjust miscoverage levels.
result Allows for trade-off between coverage and prediction set quality.
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
problem Data on unknown manifolds without boundaries.
method Finite sample bounds and asymptotic normality for kernel smoothing and its derivatives.
result Established finite sample bounds and asymptotic normality for kernel smoothing.
In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When th…
Study shows DQN's performance degrades with temporal dependence in data.
problem Temporal dependence in replayed data affects DQN's performance.
method Modelled τ τ τ -mixing data, derived risk bounds, and empirical validation. result Temporal dependence leads to a degradation in DQN's performance rate.