The curse of dimensionality affects neural network optimization, especially with smooth functions.
problem The curse of dimensionality in neural network optimization.
method Examined through the evolution of the parameter distribution under 2-Wasserstein gradient flow.
result The curse of dimensionality persists in neural network optimization, even with smooth functions.
New optimization method corrects data-driven optimizer's curse.
problem Over-optimistic evaluation in data-driven optimization.
method Smoothed f-Divergence Distributionally Robust Optimization (DRO). result Statistical bound on out-of-sample performance nearly tightest.
SCORE technique reduces BO's high-dimensional search costs.
problem Bayesian optimization's high computational costs in high-dimensional spaces.
method 1D reparametrization trick to maintain linear time complexity.
result Successfully finds global minimum in high-dimensional optimization.
New method optimizes treatment policies to avoid winner's curse.
problem Winner's curse in treatment policy optimization.
method Inference-aware policy optimization.
result Optimizes for both estimated performance and downstream evaluation.
Paper provides finite-sample guarantees for Wasserstein DRO without dimensionality curse.
problem Tackles empirical success of Wasserstein DRO in operations and ML with performance guarantees.
method Develops non-asymptotic framework for analyzing out-of-sample performance and generalization bound.
result First finite-sample guarantee for generic Wasserstein DRO problems without curse of dimensionality.
Paper shows deep neural networks can approximate Korobov functions nearly optimally.
problem Approximating Korobov functions with deep neural networks.
method Used deep neural networks and measured approximation rates with Lp and H1 norms. result Achieved a super-convergence rate, outperforming traditional methods.
Study on optimal ReLU networks with weight decay for interpolation.
problem Interpolating data with radially symmetric distributions using shallow ReLU networks.
method Weight decay regularization in infinite neuron, infinite data limit; analysis of growth rates.
result Existence and growth rates of unique radially symmetric minimizers with weight decay.
HKRR adapts to MIM, overcoming the curse of dimensionality.
problem Understanding when deep networks outperform kernel methods in high dimensions.
method Hyper-kernel ridge regression (HKRR) for multi-index models (MIM).
result HKRR can adaptively learn MIM, overcoming the curse of dimensionality.
Local Bayesian optimization shows strong performance and converges well, contrary to folklore.
problem Understanding the behavior and convergence of local Bayesian optimization methods.
method Studied the behavior of local optimization strategies and rigorously analyzed a specific algorithm.
result Local Bayesian optimization algorithms converge well and perform strongly, contrary to the folklore.
New algorithms improve convergence rates for non-log-concave sampling and log-partition estimation.
problem Efficiently sampling from non-log-concave distributions and estimating their log-partition function.
method Analysis of information-based complexity, study of polynomial-time sampling algorithms.
result Optimal rates for sampling and log-partition estimation sometimes exceed those for optimization.
Smooth DNNs mitigate the curse of dimensionality in uniform convergence for various regression tasks.
problem The curse of dimensionality in uniform convergence of ReLU networks.
method Analysis of smoothly activated deep neural networks (smooth DNNs), establishing pseudo-dimension bounds and non-asymptotic approximation guarantees.
result Smooth DNNs achieve non-asymptotic uniform convergence rates across multiple statistical contexts, mitigating the curse of dimensionality.
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm r…
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where traditional methods fail due to the curse of dimensionality.
Simple linear models outperform complex BO methods in high dimensions.
problem Overcoming the curse of dimensionality in Bayesian optimization.
method Bayesian linear regression with linear kernels, applied to high-dimensional search spaces.
result Simple linear models match or outperform state-of-the-art BO methods in high-dimensional tasks.
This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.
problem Improving approximation of fully connected deep neural networks for optimal convergence rates.
method Deriving approximation bounds specifically for a narrower fully connected deep neural network.
result Achieves an optimal rate (up to a logarithmic factor) for fully connected deep neural networks.
New findings suggest Barron space doesn't defy curse of dimensionality for certain types of smoothness.
problem Understanding the curse of dimensionality in neural networks with different smoothness notions.
method Defined ADZ spaces via Mellin transform to encapsulate nonclassical smoothness, compared to classical smoothness.
result Evidence provided that Barron space doesn't defy curse of dimensionality for certain smoothness types.
Convolutional neural networks improve image classification accuracy.
problem Improving accuracy in image classification.
method Analyzing the convergence rate of misclassification risk for image classifiers.
result A rate of convergence independent of image dimension proves the effectiveness of CNNs.
Vanilla Bayesian optimization performs well in high dimensions.
problem Bayesian optimization's poor performance in high-dimensional problems.
method Identified and addressed degeneracies, proposed scaling of Gaussian process lengthscale prior.
result Vanilla Bayesian optimization outperforms existing algorithms in high-dimensional tasks.
To overcome the curse of dimensionality and curse of modeling in Dynamic Programming (DP) methods for solving classical Markov Decision Process (MDP) problems, Reinforcement Learning (RL) algorithms are popular. In this paper, we consider an infinite-horizon average reward MDP problem and prove the optimality of the th…
Deep neural networks can solve optimal stopping problems without dimensionality issues.
problem Optimal stopping problems in high-dimensional state spaces.
method Established a general framework for deep ReLU neural networks to approximate value functions and continuation values.
result Deep neural networks can approximate value functions and continuation values with error at most ε of size κd^q ε^(-r).
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Challenges in optimizing high-dimensional, expensive functions due to the curse of dimensionality.
method GTBO combines testing and optimization phases to identify active variables and guide efficient optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional optimization tasks.
New algorithm tackles multi-agent reinforcement learning with optimal convergence rate.
problem Multi-agent reinforcement learning with large state spaces and linear function approximations.
method Refined AVLPR framework with data-dependent pessimistic estimation and action-dependent bonuses.
result First algorithm with optimal O(T−1/2) convergence rate and no poly(Amax) dependency. New method avoids curse of dimensionality in structured density estimation.
problem Estimating multivariate density with Markov graph constraints.
method Introduces 'graph resilience' to control sample complexity.
result Avoids curse of dimensionality under Markov conditions.
2D CNNs approximate Korobov functions with near-optimal rates.
problem Approximating Korobov functions using 2D CNNs.
method Constructive approach for 2D CNNs with ReLU activations and fully connected layers.
result 2D CNNs achieve near-optimal approximation rates for Korobov functions.
New MARL algorithms resolve the curse of multiagency with function approximation.
problem Challenges in Multi-Agent Reinforcement Learning (MARL) due to the curse of multiagency.
method V-Learning with Policy Replay and Decentralized Optimistic Policy Mirror Descent.
result First polynomial sample complexity results for learning approximate Coarse Correlated Equilibria (CCEs) of Markov Games under decentralized linear function approximation.
New algorithm breaks multiagency gap in robust MARL.
problem Vulnerability of MARL to sim-to-real gaps.
method Distributionally robust Markov games (RMGs) with a new uncertainty set formulation.
result First algorithm to break the curse of multiagency for RMGs.
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
This work analyzes the convergence rate of unrolling for optimizing quadratic objectives.
problem The challenge of accurately computing Jacobians through optimization.
method Non-asymptotic convergence-rate analysis of unrolled differentiation for gradient descent and Chebyshev method.
result There is a trade-off between fast asymptotic convergence and immediate but slower convergence due to the learning rate.
Max-sliced Wasserstein metric reduces high-dimensional data to 1D for better estimation.
problem Curse of dimensionality in optimal transport.
method Introduces max-sliced Wasserstein metric to reduce high-dimensional problems to 1D.
result Uniform ratio bounds of empirical measures on RKHS concentrate uniformly fast at parametric rates.
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties …
Neural networks minimize error with shallow ReLU models for function estimation.
problem Estimating unknown functions from noisy data.
method Minimizing squared errors plus weight decay regularization.
result Neural network estimators are minimax optimal up to logarithmic factors.
New algorithm tackles high-dimensional simulation optimization, converging efficiently.
problem High-dimensional simulation optimization challenges.
method Sparse grid experimental design combined with kernel ridge regression using Brownian field kernel, followed by expected improvement strategy.
result Established upper bounds on convergence rate, demonstrating superior performance in practice.
New scalable algorithm estimates barycenters of measures in high dimensions.
problem Estimating barycenters of measures in high-dimensional settings.
method Optimizes generative models to estimate barycenters, scaling by introducing inductive biases.
result First scalable method to estimate barycenters in thousands of dimensions.
Paper compares optimal denoising methods for generative models, finding different results based on data regularity.
problem Optimizing denoising in score-based generative models for various data types.
method Comparison of full-denoising and half-denoising approaches, analyzing performance in terms of distribution distances.
result Different denoising methods perform better under different data regularity conditions.
Deep neural nets can estimate regression with dependent data without the curse of dimensionality.
problem Regression with dependent data and structural assumptions on the regression function.
method Deep recurrent neural network estimate under suitable structural assumptions.
result Deep neural nets can circumvent the curse of dimensionality for regression with dependent data.
Proposes FROT for high-dimensional data, avoiding curse of dimensionality.
problem High-dimensional data challenges in optimal transport.
method Feature selection and min-max optimization for robust transport plan.
result FROT achieves state-of-the-art performance in semantic correspondence.
Improved GAS models using trees and forests for better forecasts.
problem Improving forecasts from GAS models to avoid curse of dimensionality.
method Localized parameters using decision trees and random forests.
result Significantly outperform baseline GAS model in empirical analyses.
New method circumvents curse of dimensionality in Laplacian estimation.
problem High-dimensional data challenges spectral clustering and diffusion maps.
method Kernelized Laplacian estimation via reproducing kernel Hilbert space.
result Non-asymptotic statistical rates show improved performance in high dimensions.
Riemannian Neural OT maps improve scalability on manifolds.
problem Challenges in extending neural OT to high-dimensional Riemannian manifolds.
method Introduces Riemannian Neural OT (RNOT) maps that avoid discretization and incorporate geometric structure.
result RNOT maps approximate Riemannian OT maps with sub-exponential complexity in the dimension.
Study confirms fractional norms and quasinorms do not help overcome curse of dimensionality.
problem Overcoming the curse of dimensionality in machine learning.
method Systematic testing of fractional norms and quasinorms (p<1) on classification problems.
result Distance concentration behavior is qualitatively the same for all norms and quasinorms as dimensionality increases.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
Proposes a lasso variant of MARS for nonparametric regression.
problem Nonparametric regression with MARS.
method Least squares estimation over convex function combinations with a complexity constraint.
result Achieves logarithmic convergence rate in dimensionality.
This paper tackles nonsmooth optimization in machine learning.
problem Nonsmoothness in machine learning optimization problems.
method Identifying specific structures and leveraging them for practical applications.
result Compression, acceleration, and dimension reduction are possible with nonsmooth optimization.
This paper tackles the curse of dimensionality in semi-supervised learning using Laplacian regularization.
problem The curse of dimensionality in semi-supervised learning with Laplacian regularization.
method Statistical analysis and spectral filtering methods using kernel methods.
result The paper provides a method to overcome the curse of dimensionality in semi-supervised learning.
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, a…
Data-driven decision-making often overestimates benefits due to the winner's curse.
problem Accurate policy evaluation in data-driven decision-making.
method Model-based policy evaluation using estimated models from data.
result Model-based methods can produce large, spurious reported benefits even when true effects are zero.
Study on memory effects in RNNs learning temporal data.
problem Understanding memory effects in RNNs for temporal data learning.
method Mathematical analysis of continuous-time linear RNNs, focusing on approximation and optimization dynamics.
result Long-term memory requires a large number of neurons and slows down training.
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.