Related papers: Sharper lower bounds on the performance of the emp…

The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a…

This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the…

We study the risk performance of distributed learning for the regularization empirical risk minimization with fast convergence rate, substantially improving the error analysis of the existing divide-and-conquer based distributed learning.…

A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

We consider a model where the failure hazard function, conditional on a covariate $Z$ is given by $R(t,\theta^0|Z)=\eta\_{\gamma^0}(t)f\_{\beta^0}(Z)$, with $\theta^0=(\beta^0,\gamma^0)^\top\in \mathbb{R}^{m+p}$. The baseline hazard…

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…

We study the learning performance of gradient descent when the empirical risk is weakly convex, namely, the smallest negative eigenvalue of the empirical risk's Hessian is bounded in magnitude. By showing that this eigenvalue can control…

Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

The $\ell_0$-constrained empirical risk minimization ($\ell_0$-ERM) is a promising tool for high-dimensional statistical estimation. The existing analysis of $\ell_0$-ERM estimator is mostly on parameter estimation and support recovery…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error…

For an $N \times T$ random matrix $X(\beta)$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta)$ that may depend on a possibly infinite-dimensional parameter $\beta\in \mathbf{B}$, we obtain a uniform bound on its operator…

We consider the problem of provably optimal exploration in reinforcement learning for finite horizon MDPs. We show that an optimistic modification to value iteration achieves a regret bound of $\tilde{O}( \sqrt{HSAT} + H^2S^2A+H\sqrt{T})$…

A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical…

We study Regularized Empirical Risk Minimizers (RERM) and minmax Median-Of-Means (MOM) estimators where the regularization function $\phi(\cdot)$ is an even convex function. We obtain bounds on the $L_2$-estimation error and the excess risk…

We investigate the problem of minimizing the excess generalization error with respect to the best expert prediction in a finite family in the stochastic setting, under limited access to information. We assume that the learner only has…

This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…