Related papers: Learning Convex Optimization Models
Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from exogenous features before solving. This setting is common to many real-world decision processes, and recently it…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
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 consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Inverse optimization (IO) aims to determine optimization model parameters from observed decisions. However, IO is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely…
Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…