相关论文: A new concentration result for regularized risk mi…

Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem,…

Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate…

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

In this paper, we consider high-dimensional Lp-quantile regression which only requires a low order moment of the error and is also a natural generalization of the above methods and Lp-regression as well. The loss function of Lp-quantile…

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when…

Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL…

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…

This paper investigates to what extent one can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be…

Many reinforcement learning algorithms, particularly those that rely on return estimates for policy improvement, can suffer from poor sample efficiency and training instability due to high-variance return estimates. In this paper we…

Despite widespread adoption in practice, guarantees for the LASSO and Group LASSO are strikingly lacking in settings beyond statistical problems, and these algorithms are usually considered to be a heuristic in the context of sparse convex…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. Reinforcement learning such as…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…

We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that "on average" this loss is very small, for an arbitrary compact feasible region.

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…

We propose randomized least-squares value iteration (RLSVI) -- a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value…