相关论文: Square Root Penalty: Adaptation to the Margin in C…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…
In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
Consider the domain of multiclass classification within the adversarial online setting. What is the price of relying on bandit feedback as opposed to full information? To what extent can an adaptive adversary amplify the loss compared to an…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark…
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller…
For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough…
A common way to estimate an unknown convex regression function $f_0: \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$ from a set of $n$ noisy observations is to fit a convex function that minimizes the sum of squared errors. However,…
The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso…
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the…
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing…
Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization…