Optimizes sample and round complexity in adaptive sampling from multiple distributions.
problem Adaptive sampling from multiple distributions with limited rounds and samples.
method Introduces OODS framework and analyzes tradeoffs between sample and round complexity.
result Achieves near-optimal sample complexity and sub-polynomial round complexity.
This paper improves sample complexity for AC and NAC algorithms under Markovian sampling.
problem Improving sample complexity for actor-critic and natural actor-critic algorithms.
method Characterizes convergence rate and sample complexity under Markovian sampling and mini-batch data.
result Improves sample complexity for AC and NAC algorithms by orders of magnitude.
The paper sets sample complexity bounds for identifying LTI systems from a finite set.
problem Identifying an LTI system from a finite set of possible systems using trajectory data.
method Maximum likelihood estimator and information theory tools.
result Upper and lower bounds for sample complexity are derived, independent of stability assumption.
New research determines the optimal sample complexity for multiclass and list learning.
problem Determining the optimal sample complexity for multiclass classification.
method Algebraic characterization of multiclass hypothesis classes in terms of their DS dimension.
result Proves a longstanding conjecture and determines the optimal dependence of sample complexity on DS dimension.
Unified framework for model-based RL with sample complexity guarantees.
problem Designing efficient posterior sampling methods for model-based RL.
method Optimistic posterior sampling, Hellinger distance reduction, data likelihood measurement.
result Unified algorithms with state-of-the-art sample complexity guarantees.
Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.
problem Understanding the sample complexity of Gaussian Mixture Models.
method Introducing Pair Correlation Factor (PCF) to measure clustering of component means and improving sample complexity bounds.
result The Pair Correlation Factor (PCF) more accurately determines the difficulty of parameter recovery in Gaussian Mixture Models.
Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.
problem Optimizing hypothesis testing with quantized samples and communication constraints.
method Developed a polynomial-time algorithm achieving near-optimal sample complexity under communication constraints.
result Achieved near-optimal sample complexity under communication constraints, with a logarithmic factor increase over unconstrained setting.
New method reduces sample complexity for learning Ising model dynamics exponentially.
problem Learning binary graphical models from correlated samples produced by a dynamical process.
method Two estimators based on interaction screening objective and conditional likelihood loss.
result Sample complexity reduces exponentially for samples from a dynamical process far from equilibrium.
Improves sampling, rounding, and integration of logconcave functions.
problem Sampling, rounding, and integration of logconcave functions.
method Algorithmic diffusion approach.
result First complexity improvements in nearly two decades for general logconcave functions.
New sample complexity bounds for linear predictors and neural networks, focusing on initialization.
problem Understanding sample complexity for vector-valued linear predictors and neural networks, especially under initialization-dependent conditions.
method Size-independent bounds on Frobenius norm distance from a fixed reference matrix, applying to vector-valued predictors and neural networks.
result Established new sample complexity bounds for feed-forward neural networks, resolving open questions and introducing a new learnable problem.
New algorithm reduces sample and communication complexities in federated Q-learning.
problem Optimal Q-function learning in federated Q-learning with limited communication.
method Introduced Fed-DVR-Q algorithm for order-optimal sample and communication complexities.
result Complete characterization of sample-communication complexity trade-off.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
Study shows a tradeoff between sample complexity and computational efficiency for learning halfspaces with random noise.
problem PAC learning γ-margin halfspaces with Random Classification Noise.
method Established an information-computation tradeoff and provided a simple efficient algorithm with sample complexity O(1/(γ^2 ε^2)). Also, proved lower bounds for SQ algorithms and low-degree polynomial tests.
result Inherent gap between sample complexity and computational efficiency for learning halfspaces with random noise.
Improved privacy-preserving methods for estimating multiple samples from distributions.
problem Estimating multiple samples from distributions while maintaining privacy.
method Developed new multi-sampling techniques for differentially private data estimation.
result Achieved significant reduction in sample complexity for multi-sampling from finite domains and Gaussian distributions.
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact …
Improved sample complexity for ReLU networks with norm constraints.
problem Estimating sample complexity for ReLU networks under norm constraints.
method Refined Rademacher complexity analysis for function class.
result Often no explicit depth-dependence in sample complexity bound.
New method for identifying best designs in vector optimization with uncertain feedback.
problem Optimizing vector-valued outcomes with uncertain preferences.
method Stochastic bandit feedback, polyhedral ordering cone, ( ε , δ ε,δ ε , δ )-PAC Pareto set identification. result Sample complexity characterized and matched by the naïve elimination algorithm.
Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.
problem Complexity of covariance matrix estimation for Gibbs distributions.
method Uses Markov chain Monte Carlo with conditions on the chain's spectral gap and Poincaré inequality.
result Achieves similar sample complexity as i.i.d. samples with better query complexity.
Paper resolves open problems on sample complexity in binary hypothesis testing.
problem Open problems in distributed simple binary hypothesis testing under information constraints.
method One-shot lower bound on Bayes error, streamlined sample complexity formula, reverse data-processing inequality.
result Optimally tight sample complexity bounds for communication-constrained simple binary hypothesis testing.
Improved sample complexity for training diffusion models.
problem How many samples are needed to train an accurate diffusion model?
method Analyzing the sample complexity of training diffusion models using neural networks.
result Exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other parameters.
New algorithms reduce rejection sampling complexity for shape-constrained distributions.
problem Generating exact samples from shape-constrained distributions efficiently.
method Sublinear query complexity algorithms for rejection sampling.
result Sublinear complexity algorithms for sampling from shape-constrained distributions.
New analysis shows transfer learning can significantly reduce sample size for complex models.
problem Reducing sample size needed for complex models like large language models.
method Optimal transport viewpoint applied to analyze transfer learning efficiency.
result Transfer learning can achieve better sample efficiency for complex models.
Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.
problem Identifying an unknown linear dynamical system with limited data.
method Sample complexity lower and upper bounds, persistent excitation condition, active learning algorithm.
result Lower and upper bounds share the same dependency on key problem parameters.
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
Paper analyzes sample complexity of offline MABs with KL regularization.
problem Optimizing sample complexity for offline decision-making with KL-regularized metrics.
method Sharp analysis of KL-PCB, providing upper and lower bounds.
result Characterizes sample complexity for offline MABs with KL regularization.
We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from com…
Wedge Sampling improves tensor completion with nearly-linear sample complexity.
problem Efficiently completing low-rank tensors from a subset of entries.
method Non-adaptive wedge sampling to promote structured connections in tensor completion.
result Polynomial-time algorithms achieve weak and exact recovery with nearly linear sample complexity.
New RL method reduces sample complexity for large policy spaces.
problem Large-scale RL with unknown optimal policies and state/action spaces.
method Introduces eluder dimension for policy space, proving near-optimal sample complexity.
result Near-optimal sample complexity upper bound that depends linearly on eluder dimension.
New RL method reduces sample complexity for large state-action spaces.
problem Handling large state-action spaces in RL with general Q-functions.
method Nonparametric Q-learning using kernel ridge regression.
result Sample complexity is order optimal with respect to ε and kernel complexity.
Optimal sample complexity for contrastive learning of distances.
problem Minimum labeled tuples needed for high accuracy in learning distances.
method Analyzes sample complexity in various distance settings, proving tight bounds.
result Almost optimal bound on sample complexity for learning ℓ p \ell_p ℓ p distances. Characterizes sample complexity for outcome indistinguishability in machine learning.
problem Outcome indistinguishability in machine learning, focusing on distinguishers and predictors.
method Sample complexity characterized by metric entropy of predictor and distinguisher classes, using dual Minkowski norms.
result Equivalence and tightness of sample complexity characterizations in distribution-specific and distribution-free settings.
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.
New RL theory reduces sample complexity for mixing MDPs.
problem Optimal sample complexity for reinforcement learning in mixing MDPs.
method Regeneration-type ideas to analyze mixing times.
result Optimal sample complexity depends on mixing time, not just discount factor.
New framework allows reinforcement learning with polynomial sample complexity.
problem Generalization in reinforcement learning with function approximation.
method Introduces Bilinear Classes, a structural framework for RL.
result Polynomial sample complexity for Bilinear Classes, matching best known bounds.
Paper reduces sample complexity for bilinear systems identification to nearly constant.
problem Identifying discrete-time bilinear systems under bounded disturbances.
method Uses trajectory-dependent regressors and polynomial mean-square state growth analysis.
result Proves sample complexity of O ~ ( 1 / ε ) \widetilde{\mathcal O}(1/ε) O ( 1/ ε ) for estimation error ε ε ε . Paper settles sample complexity for learning from multiple distributions.
problem Learning from multiple data distributions with a hypothesis class of bounded VC dimension.
method Introduced an algorithm with sample complexity of O((d+k)ε^-2)·(k/ε)^o(1).
result Algorithm matches lower bound up to sub-polynomial factor.
Rectified flows achieve optimal sample complexity for generating data.
problem Generating high-quality data samples efficiently.
method Rectified flows constrain transport trajectories to be linear, enabling efficient sampling.
result Achieve sample complexity of i l d e O ( ε − 2 ) ilde{O}(\varepsilon^{-2}) i l d e O ( ε − 2 ) , matching optimal rate for mean estimation. We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L_2 regularization: We introduce the γ-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the s…
Study private query release with public data, reducing sample sizes.
problem Answering a wide range of statistical queries while maintaining privacy.
method Combines public and private samples to answer queries with differential privacy.
result Private and public sample complexities for different query classes.
Paper analyzes sample complexity of polynomial neural networks.
problem Understanding the sample complexity of polynomial neural networks.
method Extends previous literature to polynomial neural networks and analyzes sample complexity.
result Obtains novel results on sample complexity of polynomial neural networks.
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.
Residual neural networks don't help overcome sampling complexity issues.
problem Learning invertible residual neural networks from samples is hard due to the curse of dimensionality.
method Investigated invertible residual neural networks and their sampling complexity.
result Invertible residual neural networks still suffer from the curse of dimensionality in sampling complexity.
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.
New findings show Rademacher complexities are not crucial for learning complexities.
problem Understanding the sample complexity of learning with squared loss in convex classes.
method Novel learning procedure combining mean estimation and Talagrand's generic chaining method.
result Sample complexity is determined by the limiting Gaussian process, not Rademacher complexities.
Paper introduces Simplet Frequency Distribution (SFD) for SCs.
problem Frequency analysis of simplets in large SCs.
method Developed SFD vector and uniform sampling-based algorithm.
result Validated theoretical bounds with experiments.
VA-LUCB identifies best arm with variance constraint, achieving optimal sample complexity.
problem Identifying the best arm with variance constraint under fixed confidence.
method Parameter-free algorithm VA-LUCB, analyzing sample complexity and proving lower bounds.
result Optimal sample complexity up to a logarithmic factor in H V A H_{VA} H V A , demonstrated by experiments. 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.
New algorithm reduces sample complexity for planning in MDPs.
problem Planning in MDPs with unknown transitions.
method MDP-GapE, a trajectory-based MCTS algorithm.
result Proves upper bound on sample complexity in terms of sub-optimality gaps.