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++.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
New analysis improves understanding of bilevel optimization stability and generalization.
problem Understanding how well bilevel optimization algorithms generalize.
method Algorithmic stability arguments and generalization bounds for three bilevel minimax solvers.
result Precise trade-off between algorithmic stability, generalization gaps, and practical settings.
Paper explores generalization of minimax learners, proposing a new metric.
problem Understanding how minimax learners perform on unseen data.
method Proposes a new metric, the primal gap, to study generalization of minimax learners.
result Derives generalization error bounds for the primal gap in nonconvex-concave settings.
Stackelberg GAN improves GAN stability by reducing minimax gap.
problem Stability issues in GAN training procedure.
method New multi-generator architecture and application of Shapley-Folkman lemma.
result Minimax gap shrinks to ε with rate O(1/ε) as the number of generators increases.
Adaptive kNN method closes the gap for unbounded support distributions.
problem Inability of standard kNN to achieve minimax optimal rate for unbounded support distributions.
method Adaptive kNN method with varying k for different samples.
result The adaptive kNN method matches the minimax lower bound.
Unified framework for corruption-robust linear bandits with optimal gap-dependent misspecification bounds.
problem Effective learning in linear bandits with corrupted rewards across different corruption models.
method Unified framework for analyzing strong and weak corruption, connection to gap-dependent misspecification, and specialized algorithm.
result Optimal bounds for gap-dependent misspecification in linear bandits.
Paper addresses eigenvector perturbation in small eigen-gap scenarios.
problem Fine-grained behavior of eigenvectors in the presence of small eigen-gaps.
method Develops de-biased estimators for linear functions of an unknown eigenvector.
result Achieves minimax lower bounds for a family of scenarios, even with small eigen-gaps.
We present a data-driven framework called generative adversarial privacy (GAP). Inspired by recent advancements in generative adversarial networks (GANs), GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrain…
New curvature measure defined for graphs, with bounds on diameter and spectral gap.
problem Defining curvature for graphs and proving its properties.
method Solving linear systems to compute curvature; applying minimax theorem.
result Graphs with positive curvature have bounded diameter and spectral gap.
Paper analyzes complexity of solving nonconvex-strongly-concave problems.
problem Finding approximate stationary points of nonconvex-strongly-concave minimax problems.
method Introduces a generic acceleration scheme to solve crafted subproblems.
result Algorithm nearly matches lower complexity bounds in general setting.
The paper explores the information-theoretic nature of excess risk in machine learning.
problem Understanding the excess risk in machine learning models.
method Formulates the minimax excess risk as a zero-sum game and modifies it to allow swapping of the order of play.
result Proves that under certain conditions, the duality gap is zero, allowing for the application of Bayesian results to provide bounds on minimax excess risk.
New algorithm reduces RL policy optimization gap.
problem Insufficient theoretical understanding of policy optimization methods.
method Reference-based Policy Optimization with Stable at Any Time guarantee (RPO-SAT)
result Achieves nearly minimax optimal policy-based algorithm for tabular RL.
Paper solves minimax optimization gap with near-optimal algorithms.
problem Designing efficient algorithms for smooth and strongly-convex-strongly-concave minimax problems.
method Accelerated proximal point method and accelerated solver for minimax proximal steps.
result First algorithm with gradient complexity matching the lower bound up to logarithmic factors.
Paper bridges theory and algorithm for domain adaptation.
problem Domain adaptation from theory to algorithm gap.
method Extended domain adaptation theories, introduced Margin Disparity Discrepancy, and transformed into adversarial learning algorithm.
result Empirical studies show state-of-the-art accuracies on domain adaptation tasks.
This paper analyzes OGDA and EG methods for nonconvex minimax problems.
problem Theoretical guarantees of OGDA and EG methods in nonconvex settings.
method Unified analysis through single-call extra-gradient methods.
result Established convergence of OGDA and EG methods under NC-SC and NC-C settings.
Optimistic algorithms achieve logarithmic regret bounds for MDPs without diameter dependence.
problem Achieving logarithmic regret bounds for episodic MDPs without relying on diameter-like quantities.
method Novel 'clipped' regret decomposition applied to optimistic algorithms.
result Smooth interpolation between gap-dependent and minimax rates of convergence.
New insights on computational limits in analyzing heterogeneous data.
problem Statistical accuracy vs computational tractability in high-dimensional heterogeneous data.
method Oracle-based computational model to establish lower bounds.
result Significant gaps between computationally feasible and classical minimax risks.
New algorithm solves complex minimax problems efficiently.
problem Minimizing and maximizing bilinearly coupled smooth functions.
method Lifted Primal-Dual (LPD) method that optimally handles both smooth and bilinear terms.
result First optimal algorithm achieving the lower complexity bound for the problem.
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
UCB algorithm's arm-sampling behavior is revealed, leading to new insights and proofs.
problem Optimizing multi-armed bandit algorithms for worst-case scenarios.
method Analysis of UCB algorithm's arm-sampling behavior and process-level characterization.
result UCB's arm-sampling rates are asymptotically deterministic, regardless of problem complexity.
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.
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.
Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.
problem Understanding convergence of GDA for nonconvex-nonconcave minimax problems.
method Local convergence analysis of GDA with stepsize ratio Θ(κ).
result Stepsize ratio of Θ(κ) is necessary and sufficient for local convergence of GDA to a Stackelberg Equilibrium.
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.
New framework for DP-SMO with near-optimal privacy-loss trade-off.
problem Optimal trade-off between privacy and population loss in DP-SMO.
method General framework using Phased-ERM method and black-box optimization.
result Near-linear time algorithms with near-optimal guarantees.
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
problem Estimating eigenvectors with small eigen-gap and fine-grained statistical reasoning.
method Eigen-decomposition of asymmetric data matrix, distribution-free procedures, adaptive to heteroscedastic noise.
result Minimax optimal under Gaussian noise, confidence intervals for eigenvalues, small eigen-gap handling.
The paper characterizes gaps in minimal foliations on tori using energy criteria.
problem Characterizing gaps in minimal foliations on tori.
method Introduced an energy to study min-max theory and applied it to Almgren-Pitts min-max theory.
result For a generic metric, if a lamination contains a gap, there exists a non-area-minimizing minimal hypersurface inside the gap.
This work analyzes machine learning for Lagrangian Relaxation in MILP.
problem Improving efficiency in solving large-scale MILP problems.
method Data-driven Algorithm Design approach to learn Lagrangian multipliers.
result Stochastic Gradient Ascent achieves the minimax optimal rate for learning multipliers.
Study on signal detection in heteroscedastic Gaussian sequences with sparse alternatives.
problem Signal detection in heterogeneous Gaussian sequences with unknown means and known covariance.
method Characterization of minimax separation radius and derivation of matching upper and lower bounds.
result Matching minimax upper and lower bounds for signal detection in heteroscedastic Gaussian sequences.
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 methods solve complex optimization problems without strong convexity assumptions.
problem Complex bilevel optimization problems with minimax lower-level structures.
method Penalty-based first-order methods for bilevel minimax optimization.
result Achieves ε ε ε -KKT point with improved oracle complexity. 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
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
New minimax optimal learner for robust predictors against adversarial examples.
problem Learning robust predictors against adversarial examples.
method Global perspective and new algorithmic ideas.
result Characterizes classes of predictors that are robustly learnable.
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…
Proposes a fairness criterion for multi-objective optimization in classification.
problem Ensuring fairness in classification models across different groups.
method Formulates a minimax Pareto fairness criterion and provides an optimization algorithm.
result Demonstrates improved fairness compared to existing methods on various real-world datasets.
New algorithms estimate Q-functions under partial coverage and realizability, improving offline RL guarantees.
problem Offline RL with limited exploration and assumptions about data coverage and Q-function realizability.
method Proposes minimax learning algorithms to estimate soft or vanilla Q-functions with L 2 L^2 L 2 -convergence guarantees. result PAC guarantees for offline RL under partial coverage and realizability conditions.
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate n − 1 / 2 n^{-1/2} n − 1/2 over multinomial and bounded-support alternatives. This research deconstructs GANs into formulation, generalization, and optimization components.
problem Improving the performance and stability of GANs.
method Proposes a perturbation view of GANs, introduces Cascade GANs, and develops principles for GAN generalization and optimization.
result Demonstrates a fundamental trade-off in GAN approximation and statistical errors, and proposes a new GAN architecture with zero minimax duality gap.
New algorithms minimize regret in multi-task and lifelong linear bandits with shared representation.
problem Minimizing regret in multi-task and lifelong linear bandits with shared representation.
method Novel algorithms using efficient estimator for low-rank linear feature extractor and novel analysis.
result Achieved regret bounds matching minimax lower bound up to logarithmic factors.
Improved reinforcement learning for episodes with varying action sets.
problem Reinforcement learning with context-dependent action sets.
method Extends MVP algorithm to handle adversarial and stochastic contexts.
result Established minimax regret bounds of O ( S A H 3 K log L ) O(\sqrt{SAH^3K\log L}) O ( S A H 3 K log L ) for adversarial contexts. PAC-Bayesian bounds show fully connected DNNs with Gaussian priors match minimax rates.
problem Theoretical limits of fully connected deep neural networks with Gaussian priors.
method PAC-Bayesian bounds for fully connected Bayesian DNNs with Gaussian priors.
result PAC-Bayesian bounds match minimax-optimal rates in Besov space for nonparametric regression and binary classification.
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…
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.
Fine-grained gap-dependent regret bounds for reinforcement learning.
problem Achieving optimal regret bounds for reinforcement learning with suboptimality gaps.
method Developed novel analytical frameworks and refined algorithms for UCB-based and non-UCB-based reinforcement learning.
result Established the first fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms.
New algorithm for non-stationary bandits with slow drifts.
problem Minimizing dynamic regret in non-stationary bandits with slowly varying rewards.
method Extends Successive Elimination to non-stationary bandits with a novel gap profile characterization.
result First instance-dependent regret upper bound for slowly varying non-stationary bandits.
Paper explores statistical and computational limits of estimating low-rank Gaussian mixtures.
problem Estimating low-rank matrix-variate observations with optimal statistical and computational limits.
method Low-rank Gaussian mixture model (LrMM) and minimax lower bounds.
result Minimax optimality of maximum likelihood estimator and spectral aggregation method.