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.
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48 results for “asymptotic sample complexity”
Paper studies robust MDPs, improving sample complexity and asymptotic performance.
problem Optimal robust policy and value function in robust MDPs with generative models.
method Improves prior results on non-asymptotic and asymptotic performances of robust MDPs, considering various uncertainty sets.
result Improved sample complexity and asymptotic normality of optimal robust value function.
This work analyzes IRM and ERM from sample complexity perspective, revealing different behaviors under various distribution shifts.
problem Choosing between IRM and ERM for OOD generalization.
method Sample complexity analysis comparing IRM and ERM under different data generation mechanisms.
result IRM is preferred over ERM for certain distribution shifts, leading to better OOD generalization.
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 method shows Hessian estimator from random samples converges to true Hessian on complex manifolds.
problem Uncertainty in Hessian estimator accuracy on complex manifolds with boundaries and nonuniform sampling.
method Locally fitting quadratic polynomials, rigorous theoretical analysis under mild conditions.
result The Hessian estimator asymptotically converges to the true Hessian, even near boundaries.
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.
Opt-BBAI identifies the best arm with minimal batches and pulls, optimizing both sample and batch complexity.
problem Batched best arm identification (BBAI) problem, aiming to minimize policy switches and resource usage.
method Proposed Opt-BBAI algorithm, achieving near-optimal sample and batch complexity in non-asymptotic settings.
result First algorithm to achieve near-optimal sample and batch complexity in non-asymptotic settings.
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.
We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexi…
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.
The paper establishes conditions for optimal sampling configurations on complex manifolds.
problem Finding optimal sampling configurations on complex manifolds.
method Analyzes point configurations on compact complex manifolds using tensor powers of Hermitian ample line bundles.
result Necessary and sufficient conditions for the existence of asymptotically Fekete sequences.
Study shows sample complexity for logistic regression with normal covariates.
problem Estimating parameters of logistic regression with normal design.
method Analyzes sample complexity in terms of dimension and inverse temperature.
result Shows two change-points in sample complexity curve based on inverse temperature.
New bounds for score matching in polynomial exponential families.
problem Understanding the sample complexity of score matching for polynomial exponential families.
method Non-asymptotic sample complexity analysis for score matching.
result First finite sample bounds for score matching in polynomial exponential families.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
Study on sample complexity for pure exploration in feedback graph settings.
problem Sample complexity of pure exploration in online learning with feedback graphs.
method Derive instance-specific lower bounds and present asymptotically optimal algorithm TaS-FG.
result TaS-FG is asymptotically optimal and efficient across different graph configurations.
This work analyzes actor-critic methods for faster convergence.
problem Finite-time analysis and sample complexity of two-time-scale actor-critic methods.
method Non-asymptotic analysis under non-i.i.d. setting, proving convergence to first-order stationary point.
result Actor-critic method finds a first-order stationary point with sample complexity.
The study reveals the efficiency of sampling from tilted distributions.
problem Sampling from a tilted distribution of an unknown underlying distribution.
method Self-normalized importance sampling to characterize accuracy.
result Polynomial vs super-polynomial sample complexity for bounded vs unbounded distributions.
In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one,…
For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a -heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…
The paper tackles efficient change point detection with limited samples.
problem Identifying multiple change points with minimal queries in noisy environments.
method Adaptive algorithm that first detects likely change points and refines their locations.
result The sample complexity is jointly governed by jump magnitudes and change point positions.
When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset…
Optimizes ICA performance in high dimensions with computational constraints.
problem Statistical optimality and computational tractability in ICA.
method Characterization of optimal sample complexity, development of computationally tractable estimates.
result Optimal sample complexity is linear in dimensionality, quadratic with low-degree polynomial algorithms.
New online method estimates OT distances from sample streams.
problem Computing OT distances between arbitrary distributions.
method Online Sinkhorn algorithm using iterative enrichment of non-parametric representation.
result Consistent estimation of true regularized OT distance with nearly-O(1/n) sample complexity.
New policy combines Thompson sampling with best challenger rule for best arm identification.
problem Best arm identification in bandit framework with fixed confidence.
method Combines Thompson sampling with best challenger rule.
result Asymptotically optimal for any two-armed bandit problems, near optimal for general K-armed bandit problems.
The paper tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.
problem Best arm identification in stochastic bandits with adversarial reward contamination.
method Proposes two algorithms: a gap-based algorithm and a successive elimination-based algorithm for sub-Gaussian bandits.
result Asymptotically optimal sample complexity for both algorithms.
New sampling algorithms for complex distributions without log-concavity.
problem Efficient sampling from complex, high-dimensional distributions.
method Randomized splitting Langevin Monte Carlo (RSLMC) algorithm.
result Uniform-in-time error bounds for RSLMC and RLMC algorithms.
New model-free RL algorithm tackles robust average-reward problems with finite sample complexity analysis.
problem Long-term decision-making in environments with varying dynamics.
method Proposes Robust Halpern Iteration (RHI) algorithm based on a black-box sampling oracle and multi-level Monte-Carlo estimator.
result Achieves ε-optimal robust policy with sample complexity of O(1/ε^(2+o(1))) under generative model setting.
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group with a …
New method identifies Condorcet winner in dueling bandits with improved sample complexity.
problem Identifying Condorcet winner in noisy pairwise comparisons.
method Exploits full gap matrix Δ to improve sample complexity.
result Improves sample complexity guarantees by leveraging informative comparisons.
Improved SV estimator for efficient data valuation.
problem Computational inefficiency in Shapley value estimation.
method Group Testing-based SV estimator with improvements.
result Enhanced asymptotic sample complexity and insights into challenges.
Paper extends Chernoff sampling for active testing and parameter estimation, improving neural network and regression models.
problem Reducing sample complexity in hypothesis testing and model parameter estimation.
method Developed an extension of Chernoff sampling for active learning and parameter estimation.
result Non-asymptotic bounds for sample complexity and estimation error in active learning.
Algorithm identifies best policy in MDPs with adaptive sampling.
problem Best policy identification in discounted MDPs with limited samples.
method Derive lower and upper bounds on sample complexity, design KLB-TS algorithm.
result KLB-TS algorithm achieves nearly-optimal sample allocation.
Active learning method balances bias and variance under class imbalance.
problem Active learning under label shift when class proportions differ.
method Mediated Active Learning under Label Shift (MALLS) using a 'medial distribution'.
result MALLS reduces asymptotic sample complexity under arbitrary label shift.
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparamet…
The effectiveness of model-based versus model-free methods is a long-standing question in reinforcement learning (RL). Motivated by recent empirical success of RL on continuous control tasks, we study the sample complexity of popular model-based and model-free algorithms on the Linear Quadratic Regulator (LQR). We show…
Develops an online Gaussian process method that maintains convergence guarantees without sample complexity issues.
problem The computational intractability of Gaussian processes with streaming data.
method Parsimonious Online Gaussian Processes (POG) that maintains asymptotic consistency with bounded memory.
result POG preserves convergence guarantees to the population posterior with finite memory, even for constant error radius.
Active learning method optimizes seismic fragility curve estimation.
problem Optimizing calls to complex numerical models for fragility curve estimation.
method Importance sampling based active learning for parametric seismic fragility curve estimation.
result The method optimizes the estimation of fragility curves with mathematical rigor.
Estimates intrinsic dimension of data for GANs.
problem Estimating intrinsic dimension of high-dimensional data.
method Uses Wasserstein distances for estimation.
result Provides sample complexity bounds for GANs.
Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.
problem Understanding optimal sample complexity for quadratic functions.
method Introduces energy allocation and optimal energy spectrum to prove tight lower bounds. Solves for Hessian-independent optimal algorithm.
result Proves optimal Hessian-dependent sample complexities and existence of a universally optimal algorithm.
We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optim…
GAAVI offers anytime-valid tests for CMF global null and contrasts.
problem Inference on the conditional mean function for high confidence decisions.
method Asymptotic anytime-valid tests for CMF global null and contrasts.
result Achieves asymptotic type-I error guarantees, power one, and optimal sample complexity.
New algorithms improve sampling from complex distributions.
problem Sampling from high-dimensional target distributions with super-linearly growing potentials.
method Proposed aHOLA and aHOLLA algorithms with non-asymptotic convergence bounds.
result Achieved state-of-the-art rates of convergence in non-convex settings.
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalm…
The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function of the Fisher information volume of the model as the sample size goes to in…
Q-learning with Uniformly Bounded Variance: Large Discounting is Not a Barrier to Fast Learningcs.LG
New Q-learning algorithm reduces sample complexity for large discount factors.
problem Large discount factors make Q-learning algorithms inefficient.
method Introduces a new Q-learning algorithm with uniformly bounded sample complexity.
result The new algorithm achieves asymptotic covariance that is a quadratic in .
New method reduces sample complexity for robust reinforcement learning.
problem Finite sample analysis in robust reinforcement learning.
method Stochastic approximation framework with controlled bias, using MLMC techniques and geometric truncation.
result Order-optimal sample complexity of for robust policy evaluation.
The paper identifies all ε-optimal arms in a bandit problem with Gaussian rewards.
problem Identifying all ε-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards.
method The paper provides two lower bounds and a Track-and-Stop strategy to solve the problem, with an efficient numerical method to solve the convex max-min program.
result The Track-and-Stop strategy has asymptotically optimal average sample complexity in the regime of low risk.
New algorithm improves RL performance across different environments.
problem Improving reinforcement learning performance across various environments.
method Designing a fully model-free DRRL algorithm that learns from a single trajectory.
result Demonstrates superior robustness and sample efficiency compared to existing methods.