Related papers: Non-convex cost functionals in boosting algorithms…

This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…

In this article we propose a boosting algorithm for regression with functional explanatory variables and scalar responses. The algorithm uses decision trees constructed with multiple projections as the "base-learners", which we call…

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…

This paper examines the role and efficiency of the non-convex loss functions for binary classification problems. In particular, we investigate how to design a simple and effective boosting algorithm that is robust to the outliers in the…

We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear,…

Boosting has emerged as a useful machine learning technique over the past three decades, attracting increased attention. Most advancements in this area, however, have primarily focused on numerical implementation procedures, often lacking…

We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization…

We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…

This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able…

Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

Energy price forecasting is a relevant yet hard task in the field of multi-step time series forecasting. In this paper we compare a well-known and established method, ARMA with exogenous variables with a relatively new technique Gradient…

We consider the problem of forecasting the aggregate demand of a pool of price-responsive consumers of electricity. The price-response of the aggregation is modeled by an optimization problem that is characterized by a set of marginal…

Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…

Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…

A nonlinear regression framework is proposed for time series and panel data for the situation where certain explanatory variables are available at a higher temporal resolution than the dependent variable. The main idea is to use the moments…

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between…