Study minimax-optimal rates for offline decision-making with function approximation.
problem Statistical complexity of offline decision-making with function approximation.
method Near minimax-optimal rates for stochastic contextual bandits and Markov decision processes, using pseudo-dimension and behavior policy.
result Established performance limits and new characterization of behavior policy.
A novel decentralized algorithm improves minimax optimization in federated learning.
problem Minimax optimization in federated learning with data heterogeneity.
method Decentralized Gradient Tracking (K-GT-Minimax) for nonconvex-strongly-concave optimization.
result Demonstrates superior convergence rate for NC-SC minimax optimization.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
We study the minimax optimal rate for estimating the Wasserstein- 1 1 1 metric between two unknown probability measures based on n n n i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures u…
The paper optimizes k-NN for distributed learning with minimax optimal performance.
problem Minimizing error rates in classification, regression, and density estimation.
method Optimal aggregation of fixed-k nearest neighbors from multiple subsets of data.
result Achieves minimax optimal error rates up to a logarithmic factor.
Classical scaling is shown to be optimal under various noisy conditions.
problem Consistency of classical scaling under general noise conditions.
method Established using finite fourth moments of noise, derived convergence rates, and matching minimax lower bounds.
result Classical scaling achieves minimax optimality in recovering true configuration from noisy dissimilarities.
In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the d…
The paper constructs optimal confidence bands for kernel gradient flow estimators.
problem Estimating generalization error and constructing confidence bands for kernel gradient flows.
method Established convergence rates and constructed optimal confidence bands under capacity-source condition.
result Optimal confidence bands for kernel gradient flows have shrinkage rates close to minimax optimal rates.
Study on DiTs' rates of approximation and estimation under various data assumptions.
problem Investigating statistical rates of conditional diffusion transformers.
method Discretization and Taylor expansion of conditional diffusion score function under Hölder smooth data assumption.
result Establishes statistical limits for conditional and unconditional DiTs, offering practical guidance.
Kernel estimator optimally recovers function from noisy exponential Radon transform.
problem Inverting noisy exponential Radon transform of a function.
method Proposed a kernel estimator to estimate the true function.
result The estimator converges to the true function at minimax optimal rate.
Paper analyzes kNN estimator for KL divergence, proving its optimality.
problem Estimating KL divergence from identical samples.
method kNN estimator based on nearest neighbor distances.
result kNN method is asymptotically rate optimal for KL divergence estimation.
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high dimensional problems. In the {\it sparse regime} when the components are sufficientl…
Shallow neural networks can represent polynomials efficiently.
problem Representing polynomials using shallow neural networks.
method Using shallow neural networks of width 2 ( R + d ) d 2(R+d)^d 2 ( R + d ) d to represent d d d -variate polynomials of degree R R R . result Derives minimax optimal convergence rate for shallow networks to unknown univariate regression functions.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
Optimizes identifying the best arm with fixed samples.
problem Finding the arm with the highest mean in a fixed number of samples.
method Characterizes minimax optimal rates and introduces algorithms to achieve them.
result Characterizes and introduces algorithms for optimal best arm identification.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on n n n independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probabili…
New SGDA method speeds up nonconvex minimax optimization.
problem Improving convergence of nonconvex minimax optimization.
method SGDA with random reshuffling for nonconvex-PŁ objectives.
result Convergence rates faster than with-replacement SGDA.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
Sampling without replacement speeds up optimization in minimax problems.
problem Optimizing minimax problems with faster convergence rates.
method Analysis of gradient descent ascent and proximal point method with two sampling strategies.
result Sampling without replacement leads to faster convergence rates in minimax optimization.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…
New algorithms improve convergence of minimax optimization.
problem Minimax optimization convergence issues in nonconvex problems.
method Established new convergence results for two single-loop algorithms.
result Improved convergence rates for minimax optimization.
Study on CNNs' learning rates and approximation capacities.
problem Learning rates and approximation capacities of CNNs.
method New approximation bound and covering number analysis for CNNs.
result Derives minimax optimal convergence rates for CNNs in various learning problems.
Paper proposes a transfer learning method for improving matrix completion.
problem Improving estimation of a low-rank target matrix using auxiliary data.
method Transfer learning procedure leveraging prior information on favorable source datasets.
result Method outperforms traditional methods when source datasets are close to the target matrix.
We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be noisy or even completely missing in a stochastic manner. To this end, we propose…
Kernel method improves instrumental variable regression rates.
problem Nonparametric instrumental variable regression with weak instruments.
method Kernel-based two-stage least-squares method, strong L 2 L_2 L 2 convergence analysis. result Minimax optimal rates for instrumental regression under standard assumptions.
The paper improves Gaussian process regression by optimizing hyperparameters.
problem Hyperparameter tuning for Gaussian process regression models.
method Adaptive sparse variational approximations using variational Bayes.
result Minimax optimal rates of convergence for variational posterior.
This paper studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of n n n vertices…
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.
The paper proves neural networks' consistency and optimal convergence rates for various function classes.
problem Proving neural networks' consistency and optimal convergence rates for diverse function classes.
method Analyzes wide and deep ReLU neural networks trained on logistic loss and Kolmogorov-Donoho optimal function classes.
result Proves universal consistency and minimax optimal convergence rates for neural networks.
New method estimates hidden binary mixture model centers efficiently.
problem Estimating centers in high-dimensional binary mixture models with hidden Markov structure.
method Proposes a minimax optimal procedure and an adaptive variant.
result Achieves optimal rate of order δ d / n + d / n \sqrt{δd/n} + d/n δ d / n + d / n . Paper studies minimax optimal regression using Laplacian smoothing over graphs.
problem Minimax optimal regression over Sobolev spaces.
method Laplacian smoothing on neighborhood graphs.
result Upper bounds match minimax optimal rates for first-order Sobolev class.
Paper introduces SGD for nonparametric additive models with optimal risk.
problem Training nonparametric additive models efficiently and accurately.
method Iterative algorithm based on stochastic gradient descent for truncated basis expansions.
result Estimator achieves minimax optimal risk in well-specified settings.
Develops a minimax optimal estimator for system stability under distribution shift.
problem Ensuring system reliability under changes in the underlying environment.
method Minimax optimal estimation of stability defined in terms of acceptable performance degradation.
result Characterizes the minimax convergence rate and demonstrates practical utility.
Study confirms learning rates for vector-valued spectral algorithms, proving consistency.
problem Theoretical confirmation of learning rates for vector-valued spectral algorithms.
method Rigorous analysis of learning rates for various vector-valued spectral algorithms, including kernel ridge regression and gradient descent.
result Upper and lower bounds on learning rates for vector-valued spectral algorithms, proving minimax optimality in various scenarios.
Gradient Descent with Projection learns low-degree polynomials efficiently.
problem Learning low-degree spherical polynomials with neural networks.
method Over-parameterized two-layer neural network with Gradient Descent with Projection.
result Achieves nearly minimax optimal sample complexity and risk bound.
Gradient descent methods for deep ReLU networks achieve optimal generalization rates.
problem Generalization of gradient descent methods for deep neural networks
method Establishing minimax-optimal rates for GD and SGD with deep ReLU networks
result Gradient descent methods for deep ReLU networks achieve optimal generalization rates
Bayesian analysis shows unlabeled data improve graph-based semi-supervised learning.
problem Improving semi-supervised learning with limited labeled data.
method Bayesian nonparametric approach using unlabeled data for graph-based learning.
result Posterior contracts optimally around the truth with sufficient unlabeled data.
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of init…
Transformers can efficiently approximate nonparametric regression with minimal parameters and sequences.
problem Efficiently approximating nonparametric regression functions with transformers.
method Kernel-weighted polynomial basis and gradient descent.
result Achieves minimax optimal rate of convergence with fewer parameters and sequences.
Paper calculates eigenvalue decay rates for neural network kernels on general domains.
problem Determining eigenvalue decay rates for neural network kernels on arbitrary domains.
method Proved dynamics of wide neural networks approximates NTK on general domains, used minimax optimality and interpolation spaces.
result Provided strategy to calculate eigenvalue decay rates for neural network kernels.
Paper proposes robust estimators for GANs under Wasserstein contamination.
problem Robust estimation of distributions under contamination.
method Wasserstein GAN-based estimators for location, covariance, and regression.
result Proposed estimators are minimax optimal in many scenarios.
This paper studies first order methods for solving smooth minimax optimization problems min x max y g ( x , y ) \min_x \max_y g(x,y) min x max y g ( x , y ) where g ( ⋅ , ⋅ ) g(\cdot,\cdot) g ( ⋅ , ⋅ ) is smooth and g ( x , ⋅ ) g(x,\cdot) g ( x , ⋅ ) is concave for each x x x . In terms of g ( ⋅ , y ) g(\cdot,y) g ( ⋅ , y ) , we consider two settings -- strongly convex and nonconvex -- and improve upon the best known rates in both. …
This paper improves the convergence rates of bilevel optimization algorithms.
problem Improving the convergence rates of bilevel optimization algorithms.
method Provided lower complexity bounds and proposed an accelerated bilevel optimizer.
result AccBiO achieves optimal results under certain conditions.
GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.
problem The suboptimality of GP-UCB under polynomial effective optimism.
method Analysis of effective optimism level and new regret lower bound.
result GP-UCB is not minimax optimal under polynomial growth of effective optimism.