New fairness concept extends minimax fairness to lexicographic fairness.
problem Fairness in supervised learning, especially lexicographic fairness.
method Introduced approximate lexifairness, derived algorithms for finding solutions, and proved generalization bounds.
result Proved that approximate lexifairness on training data implies approximate lexifairness on true distribution.
UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method UCRL2-VTR algorithm with Bernstein-type bonus.
result Achieves a regret of i l d e O ( d D T ) ilde{O}(d\sqrt{DT}) i l d e O ( d D T ) with matching lower bound. 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.
Improved gap-dependent bounds for reinforcement learning with linear approximations.
problem Achieving nearly minimax-optimal performance with linear function approximation.
method Developed and analyzed the LSVI-UCB++ algorithm and its concurrent variant.
result First gap-dependent regret bound for nearly minimax-optimal algorithm LSVI-UCB++.
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.
We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth manifold, in a cost-sensitive setting. This generalises a classic result of Audibert an…
The paper identifies network bottlenecks using minimax paths in stochastic networks.
problem Identifying bottlenecks in networks with stochastic weights.
method Modeling as combinatorial semi-bandit problem, applying combinatorial Thompson Sampling, and approximating the original objective due to computational intractability.
result Established an upper bound on Bayesian regret and evaluated Thompson Sampling performance on real-world networks.
Pessimistic Minimax Value Iteration finds efficient NE policies from offline data.
problem Finding an approximate Nash equilibrium in offline Markov games with non-uniform coverage.
method Pessimistic Minimax Value Iteration (PMVI) constructs pessimistic value function estimates and solves NEs.
result Established a nearly minimax optimal result for offline Markov games with function approximation.
New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.
problem Offline RL with linear function approximation in MDPs and MGs.
method Pessimism-based algorithm with uncertainty decomposition via reference function.
result Nearly minimax optimal performance in offline RL for MDPs and MGs.
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.
New algorithms tackle robust RL with linear models, revealing unique challenges.
problem Distributionally robust offline RL with uncertainty in dynamics.
method Proposes minimax optimal and computationally efficient algorithms using novel function approximation mechanisms.
result Function approximation in robust offline RL is distinct and harder than in standard offline RL.
The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.
problem Estimating weights and quality functions in reinforcement learning with function approximation.
method The paper uses minimax methods for estimating marginal importance weights and q-functions.
result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.
Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of parameters are precisely non-zero. This excludes models where linear formulations…
This paper explores minimax-Bayes solutions for reinforcement learning problems.
problem How to select appropriate priors for decision making under uncertainty in sequential decision making.
method Study of minimax-Bayes solutions for various reinforcement learning problems.
result Minimax policies are more robust than standard priors.
Paper proves Sion's theorem in geodesic spaces and develops a Riemannian extragradient method.
problem Understanding saddle points in nonconvex-nonconcave minimax problems.
method Geodesic metric space version of Sion's theorem and Riemannian extragradient method.
result Developed a Riemannian extragradient algorithm for smooth minimax problems.
The paper analyzes rates of approximation for eigenpairs of Laplace-Beltrami operators on manifolds.
problem Estimating eigenpairs of elliptic differential operators from manifold samples.
method Analyzes minimax rates for eigenvalue and eigenvector estimation using graph Laplacians.
result The minimax rate for H 1 ( M ) H^1(M) H 1 ( M ) -sense approximation is n − 2 / ( d + 4 ) n^{-2/(d+4)} n − 2/ ( d + 4 ) . New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
New RL algorithm for linear MDPs with nearly optimal regret.
problem Optimizing reinforcement learning for linear mixture Markov decision processes.
method Proposed a new Bernstein-type concentration inequality for self-normalized martingales and a computationally efficient algorithm UCRL-VTR+.
result UCRL-VTR+ achieves nearly minimax optimal regret of i l d e O ( d H T ) ilde O(dH\sqrt{T}) i l d e O ( d H T ) . New algorithm ranks players from partial comparisons with optimal rate.
problem Ranking players from partial pairwise comparisons.
method Divide-and-conquer approach, local MLE within groups.
result Optimal ranking algorithm with minimax rate.
Study on RNNs' ability to approximate past-dependent Hölder functions and their application to regression.
problem Understanding and optimizing the approximation capacity of RNNs for regression tasks.
method Derivation of upper bounds on RNN approximation error for Hölder smooth functions and application to regression.
result Achievement of minimax optimal prediction error bounds for RNNs under various data assumptions.
Novel methods for accelerating optimization in complex bilevel and minimax problems.
problem Optimization challenges in bilevel and minimax problems, especially when strong convexity assumptions are not met.
method Accelerated fully first-order methods for Bilevel Optimization (BLO) and Minimax Optimization (NCSC).
result State-of-the-art complexity for finding approximate second-order stationary points in BLO and NCSC.
This paper optimizes off-policy evaluation in reinforcement learning with function approximation.
problem Estimating cumulative value of a new policy from logged data generated by an unknown policy.
method Regression-based fitted Q iteration method, equivalent to estimating conditional mean embedding of transition operator.
result The method is minimax-optimal, with nearly minimal estimation error.
This paper tackles convex-submodular minimax problems in mixed continuous-discrete domains.
problem Convex-submodular minimax problems in mixed continuous-discrete domains.
method Introduces new notions of optimality and proposes iterative algorithms combining discrete and continuous optimization.
result Characterizes convergence rates, computational complexity, and quality of solutions for convex and monotone-submodular minimax problems.
Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.
problem Empirical success of SGD in semi-discrete OT, but lack of theoretical guarantees.
method Averaged projected SGD with a minimax convergence rate of O(1/√n).
result SGD methods can estimate the OT map with a minimax convergence rate of O(1/√n).
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.
Standard Transformers approximate Hölder functions and achieve optimal nonparametric regression rate.
problem Approximating Hölder functions and achieving optimal nonparametric regression rate with Transformers.
method Using the size tuple and dimension vector metrics, the paper characterizes Transformer structures and derives upper bounds for their Lipschitz constant and memorization capacity.
result Standard Transformers achieve the minimax optimal rate in nonparametric regression for Hölder target functions.
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n n n samples, the time and space complexity of computing the KRR estimate scale as O ( n 3 ) \mathcal{O}(n^3) O ( n 3 ) and O ( n 2 ) \mathcal{O}(n^2) O ( n 2 ) respectively, and so is prohibitive in many cases. We prop…
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
New theorem guarantees approximate equilibrium in non-convex games.
problem No guarantee of equilibrium in non-convex games.
method Introduced a minimax theorem for non-convex games involving neural networks.
result Provided an approximate minimax theorem for non-convex games.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
problem RL with linear function approximation lacks uniform-PAC guarantees.
method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.
result Uniform-PAC convergence to optimal policy with high probability.
New RL algorithm tackles nonstationary MDPs with linear approximations and varying rewards.
problem Nonstationary reinforcement learning with evolving reward and state transition functions.
method Developed a new algorithm LSVI-UCB-Restart with periodic restart, and parameter-free Ada-LSVI-UCB-Restart for unknown variation budgets.
result First minimax dynamic regret lower bound for nonstationary linear MDPs and linear MDPs lower bound.
Proves minimax sample complexity for turn-based stochastic games.
problem Proving theoretical guarantees for reinforcement learning in turn-based stochastic games.
method Developing absorbing TBSG and reward perturbation techniques to handle statistical dependence.
result Empirical Nash equilibrium strategy approximates true Nash equilibrium in turn-based stochastic games.
Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult to obtain via optimization due to sparse constraints in important function class…
Paper analyzes minimax risks of personalized federated learning algorithms.
problem Statistical heterogeneity among clients in federated learning.
method Minimax analysis of FedAvg and local training approaches.
result Threshold for optimality between FedAvg and local training depends on data heterogeneity.
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in L q L_q L q -norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
A new test for comparing distributions is proposed, balancing optimality and efficiency.
problem Comparing distributions defined over non-Euclidean domains.
method Spectral-regularized two-sample test based on random Fourier features.
result The proposed test is minimax optimal under certain conditions.
Quantile regression with ReLU networks achieves minimax rates for various function types.
problem Estimating quantiles from covariates with neural networks.
method Quantile regression with rectified linear unit (ReLU) neural networks.
result ReLU networks achieve minimax rates for broad collections of function types.
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.
New algorithm reduces RL complexity with low switching costs.
problem Exploration-exploitation dilemma in RL with complex models.
method Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation.
result Achieves minimax optimal regret of O ( d H K ) O(d\sqrt{HK}) O ( d H K ) and near-optimal policy switching cost. Transformers learn new tasks from few examples via optimal approximation.
problem Learning new tasks from limited examples using large language models.
method Developed approximation and generalization error bounds for transformers trained on nonparametric regression tasks.
result Transformers achieve minimax optimal estimation risk in context.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
New analysis of stochastic approximation with non-expansive mappings.
problem Finite-time analysis of two-time-scale stochastic approximation with non-expansive mappings.
method Studied two-time-scale stochastic approximation algorithms with non-expansive mappings and projection steps.
result Last-iterate mean square residual error decays at a rate O ( 1 / k 1 / 4 − ε ) O(1/k^{1/4-ε}) O ( 1/ k 1/4 − ε ) . New method tackles nonconvex-nonconcave problems with local KL condition.
problem Nonconvex-nonconcave minimax problems under varying KL conditions.
method Inexact proximal gradient method for KL-structured subproblems.
result Complexity guarantees for approximate stationary points.
It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear aggregation approaches motivated by regression applications. We show that the proposed a…
An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance ba…
The paper analyzes contraction rates for GP regression approximations.
problem Computational infeasibility of exact GP posterior in large-scale applications.
method Lanczos and conjugate gradient approximations of the posterior mean.
result Minimax contraction rates for these approximations in large-scale applications.