Related papers: $L_p$ regularized portfolio optimization

Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim…

$L_p$-norm regularization schemes such as $L_0$, $L_1$, and $L_2$-norm regularization and $L_p$-norm-based regularization techniques such as weight decay, LASSO, and elastic net compute a quantity which depends on model weights considered…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…

There has been an explosion of interest in using $l_1$-regularization in place of $l_0$-regularization for feature selection. We present theoretical results showing that while $l_1$-penalized linear regression never outperforms…

The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics.…

We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…

Discount regularization, using a shorter planning horizon when calculating the optimal policy, is a popular choice to restrict planning to a less complex set of policies when estimating an MDP from sparse or noisy data (Jiang et al., 2015).…

Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to…

Recently, $L_1$ regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, $L_1$ regularization…

Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…

Policy optimization (PO) is a key ingredient for reinforcement learning (RL). For control design, certain constraints are usually enforced on the policies to optimize, accounting for either the stability, robustness, or safety concerns on…

In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$…

A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As…

We study the performance of empirical risk minimization on the $p$-norm linear regression problem for $p \in (1, \infty)$. We show that, in the realizable case, under no moment assumptions, and up to a distribution-dependent constant,…