arXiv research

Study on estimating invertible functions with minimax analysis.

This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the…

This paper analyzes OGDA and EG methods for nonconvex minimax problems.

We prove a new minimax theorem connecting the worst-case Bayesian regret and minimax regret under partial monitoring with no assumptions on the space of signals or decisions of the adversary. We then generalise the information-theoretic tools of Russo and Van Roy (2016) for proving Bayesian regret bounds and combine th…

New analysis improves understanding of bilevel optimization stability and generalization.

A novel decentralized algorithm improves minimax optimization in federated learning.

Efficient sampling reduces memory usage for Minimax distance analysis.

Paper proposes an algorithm to solve complex minimax problems efficiently.

We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the functi…

Paper investigates optimal transport map estimation in infinite-dimensional spaces.

We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on these rules, we obtain data-dependent performance guarantees without distributio…

Unified analysis of efficient local training methods for distributed variational inequalities.

This paper analyzes saddle points and minimax points in non-convex smooth games.

New estimator achieves minimax optimal risk in transfer learning.

Paper analyzes how unlabeled data improves SSL and adversarial robustness.

We find the optimal error for a constrained regression model under a linear model.

Study stabilizes adversarial training in neural networks over infinite-dimensional spaces.

TiAda adapts adaptive gradient methods for nonconvex minimax optimization.

This study improves estimation of the first principal component in multivariate functional data.

Paper improves risk bounds for nonconvex-strongly-concave minimax problems.

Paper addresses eigenvector perturbation in small eigen-gap scenarios.

Paper explores generalization of minimax learners, proposing a new metric.

Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.

A federated minimax framework for heterogeneous clients.

New RL method nearly optimally learns policies with generative models.

New algorithm solves minimax games with linear constraints.

While crowdsourcing has become an important means to label data, there is great interest in estimating the ground truth from unreliable labels produced by crowdworkers. The Dawid and Skene (DS) model is one of the most well-known models in the study of crowdsourcing. Despite its practical popularity, theoretical error …

The paper analyzes how optimization algorithms affect the generalization of minimax models.

The paper analyzes kNN density estimation's convergence rates under different conditions.

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…

Improved FTPL algorithm reduces regret in predictable minimax games.

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial learning problem can be reduced to a minimax statistical learning problem by intr…

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under W…

This paper analyzes neural networks for solving complex optimization problems.

Study on optimal rates for sequential probability assignment using smoothed analysis.

The paper tackles robust policy learning from multiple data sources.

New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.

Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.

New algorithms solve complex minimax problems without needing derivatives.

In adaptive data analysis, the user makes a sequence of queries on the data, where at each step the choice of query may depend on the results in previous steps. The releases are often randomized in order to reduce overfitting for such adaptively chosen queries. In this paper, we propose a minimax framework for adaptive…

Study on DiTs' rates of approximation and estimation under various data assumptions.

We study the problem of switching-constrained online convex optimization (OCO), where the player has a limited number of opportunities to change her action. While the discrete analog of this online learning task has been studied extensively, previous work in the continuous setting has neither established the minimax ra…

This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active …

New RL algorithm minimizes distributional learning error.

SDP achieves optimal error in noisy phase synchronization.

The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.

We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the minimax expected regret is $Ω(\sqrt{dT (\log T) (\log n)})$ for every algorithm, and (2) introduce a V…

Sampling without replacement speeds up optimization in minimax problems.