arXiv research

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

The paper analyzes generalization bounds for NC-SC/NC-C stochastic minimax optimization.

Study minimax linear regression under quantile risk, improving existing bounds and providing new results.

Develops high-probability minimax quantile bounds for statistical problems.

New bounds on minimax regret for sequential probability assignment using logarithmic loss.

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…

New algorithms for private GLM estimation with minimax lower bounds.

New research sets the minimax lower bound for KSD estimation at sqrt(n).

The study establishes minimax bounds for estimating operators from noisy samples.

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…

GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

Study exact minimax rates for density estimation over convex classes, extending previous work.

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

Study minimax regret in sequential probability assignment with and without side information.

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

Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.

Score attack method provides a lower bound on privacy-constrained minimax risk.

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…

New algorithms solve complex minimax problems without needing derivatives.

The paper optimizes risk-sensitive RL with CVaR, achieving near-minimax-optimal results.

We develop a new theoretical framework, the \emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional $\ell_1$-balls within a factor of two. The prior is newly derived for achieving the mini…

Develops locally private methods for nonparametric contextual bandits.

Improved gap-dependent bounds for reinforcement learning with linear approximations.

We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order $d/n$ in dimension $d$ with $n$ samples. Here, we study the minimax expected excess risk over the full linear class, depending on the dist…

New SGDA method speeds up nonconvex minimax optimization.

Study on kernel regression risk in high dimensions using Pinsker bound.

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 …

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied s…

Paper improves algorithms for convex-concave minimax optimization problems.

k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has bounded support and the probability density function is bounded away from zero in i…

Optimal algorithm for linear bandits on ellipsoids with minimax regret bound.

Paper explores fair classification with bounded disparity using finite datasets.

Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.

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

Study minimax regret in bilateral trade with heavy-tailed valuations.

Deep neural networks are optimal for dependent data using PAC-Bayes bounds.

Paper proposes an algorithm to solve complex minimax problems efficiently.

Neural networks minimize error with shallow ReLU models for function estimation.

Thompson sampling is one of the most widely used algorithms for many online decision problems, due to its simplicity in implementation and superior empirical performance over other state-of-the-art methods. Despite its popularity and empirical success, it has remained an open problem whether Thompson sampling can match…

New bounds show simple predictors can learn complex concepts online.

Study finds optimal regret bound for multi-armed bandit problem with expert advice.

Study confirms optimal minimax rate for nonlocal interaction kernel estimation.

New fairness concept extends minimax fairness to lexicographic fairness.

The paper develops a minimax optimal method for high-dimensional regression using auxiliary data.

We analyze the Kozachenko--Leonenko (KL) nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance over Hölder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a new minimax lower bound over the Hölder ba…

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…