Related papers: Empirical entropy, minimax regret and minimax risk
Reinforcement learning from human feedback (RLHF) replaces hard-to-specify rewards with pairwise trajectory preferences, yet regret-oriented theory often assumes that preference labels are generated consistently from a single ground-truth…
Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class…
State-of-the-art efficient model-based Reinforcement Learning (RL) algorithms typically act by iteratively solving empirical models, i.e., by performing \emph{full-planning} on Markov Decision Processes (MDPs) built by the gathered…
Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…
We study minimax rates for high-dimensional linear regression with additive errors under the $\ell_p\ (1\leq p<\infty)$-losses, where the regression parameter is of weak sparsity. Our lower and upper bounds agree up to constant factors,…
This paper addresses the challenge of integrating sequentially arriving data within the quantile regression framework, where the number of features is allowed to grow with the number of observations, the horizon is unknown, and memory is…
We study model-based reinforcement learning in an unknown finite communicating Markov decision process. We propose a simple algorithm that leverages a variance based confidence interval. We show that the proposed algorithm, UCRL-V, achieves…
Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is presented under mild conditions on $f$. Under such conditions, the optimal measure is shown to be unique. Examples of the solution for particular…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data,…
We consider statistical learning problems, when the distribution $P'$ of the training observations $Z'_1,\; \ldots,\; Z'_n$ differs from the distribution $P$ involved in the risk one seeks to minimize (referred to as the test distribution)…
The effect of the relative entropy asymmetry is analyzed in the empirical risk minimization with relative entropy regularization (ERM-RER) problem. A novel regularization is introduced, coined Type-II regularization, that allows for…
We establish a new concentration result for regularized risk minimizers which is similar to an oracle inequality. Applying this inequality to regularized least squares minimizers like least squares support vector machines, we show that…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…
In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…
Probabilistic classifiers are central for making informed decisions under uncertainty. Based on the maximum expected utility principle, optimal decision rules can be derived using the posterior class probabilities and misclassification…
We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted $Q$-iteration…
Differentially private empirical risk minimization (DP-ERM) is a fundamental problem in private optimization. While the theory of DP-ERM is well-studied, as large-scale models become prevalent, traditional DP-ERM methods face new…