Related papers: Modeling an Augmented Lagrangian for Blackbox Cons…
Optimization of problems with high computational power demands is a challenging task. A probabilistic approach to such optimization called Bayesian optimization lowers performance demands by solving mathematically simpler model of the…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
Bayesian Optimization, leveraging Gaussian process models, has proven to be a powerful tool for minimizing expensive-to-evaluate objective functions by efficiently exploring the search space. Extensions such as constrained Bayesian…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to…
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
In this two-part study, we develop a general theory of the so-called exact augmented Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to traditional nonsmooth exact penalty functions, these augmented…
We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…