Related papers: Analytic approach to variance optimization under a…
It is important for a portfolio manager to estimate and analyze recent portfolio volatility to keep the portfolio's risk within limit. Though the number of financial instruments in the portfolio can be very large, sometimes more than…
We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…
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).…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking…
We address a class of integer optimization programs with a total variation-like regularizer and convex, separable constraints on a graph. Our approach makes use of the Graver basis, an optimality certificate for integer programs, which we…
This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
In this paper, we investigate a group sparse optimization problem via $\ell_{p,q}$ regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue…
This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…
Online mirror descent (OMD) is a fundamental algorithmic paradigm that underlies many algorithms in optimization, machine learning and sequential decision-making. The OMD iterates are defined as solutions to optimization subproblems which,…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…