Related papers: Empirical entropy, minimax regret and minimax risk

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

We obtain risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex. Results for the ERM are derived without assumptions on the outputs and under…

The upper confidence reinforcement learning (UCRL2) algorithm introduced in (Jaksch et al., 2010) is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite…

This paper studies regret minimization with randomized value functions in reinforcement learning. In tabular finite-horizon Markov Decision Processes, we introduce a clipping variant of one classical Thompson Sampling (TS)-like algorithm,…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

We study the problem of estimating Dynamic Discrete Choice (DDC) models, also known as offline Maximum Entropy-Regularized Inverse Reinforcement Learning (offline MaxEnt-IRL) in machine learning. The objective is to recover reward or $Q^*$…

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…

Reinforcement learning (RL) in large environments often suffers from severe computational bottlenecks, as conventional regret minimization algorithms require repeated, costly calls to planning and statistical estimation oracles. While…

We study the problem of sequential probability assignment under logarithmic loss, both with and without side information. Our objective is to analyze the minimax regret -- a notion extensively studied in the literature -- in terms of…

We study the problem of reinforcement learning in infinite-horizon discounted linear Markov decision processes (MDPs), and propose the first computationally efficient algorithm achieving rate-optimal regret guarantees in this setting. Our…

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

Motivated by several examples, we consider a general framework of learning with linear loss functions. In this context, we provide excess risk and estimation bounds that hold with large probability for four estimators: ERM, minmax MOM and…

The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…

We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the class has a subexponential envelope…

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…

Reinforcement learning (RL) has traditionally been understood from an episodic perspective; the concept of non-episodic RL, where there is no restart and therefore no reliable recovery, remains elusive. A fundamental question in…

In this paper, we study the estimation performance of empirical $\ell_2$ risk minimization (ERM) in noisy (standard) phase retrieval (NPR) given by $y_k = |\alpha_k^*x_0|^2+\eta_k$, or noisy generalized phase retrieval (NGPR) formulated as…

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…

This paper proposes a versatile covariate adjustment method that directly incorporates covariate balance in regression discontinuity (RD) designs. The new empirical entropy balancing method reweights the standard local polynomial RD…

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…