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High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

A large portfolio of independent returns is optimized under the variance risk measure with a ban on short positions. The no-short selling constraint acts as an asymmetric $\ell_1$ regularizer, setting some of the portfolio weights to zero…

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be…

We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which…

Several applications of Reinforcement Learning suffer from instability due to high variance. This is especially prevalent in high dimensional domains. Regularization is a commonly used technique in machine learning to reduce variance, at…

This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…

In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originates the algorithms to…

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of…

Markowitz's criterion aims to balance expected return and risk when optimizing the portfolio. The expected return level is usually fixed according to the risk appetite of an investor, then the risk is minimized at this fixed return level.…

Due to the poor generalization performance of traditional empirical risk minimization (ERM) in the case of distributional shift, Out-of-Distribution (OoD) generalization algorithms receive increasing attention. However, OoD generalization…

Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…

Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…

The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use…

This paper develops a sparsity-promoting integral concurrent learning (SP-ICL) adaptation law for a linearly parametrized uncertain nonlinear control-affine system. The unknown parameters are learned using ICL with sparsity-promoting…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

Emergent behaviors are in the focus of recent research interest. It is then of considerable importance to investigate what optimizations suit the learning and prediction of chaotic systems, the putative candidates for emergence. We have…

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…

In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…

We show that regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis. We develop a procedure that jointly regularizes expectations and variance-covariance matrices using a pair of shrinkage priors.…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…